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Permutation and CombinationQuestion and Answers: Page 22

Question Number 26477 Answers: 1 Comments: 0

A number of four different digits is formed by using the digits 1,2,3,4,5,6,7,in all possible ways each digit occuring once only.find how many of them are greater than 3400

$A n u m b e r o f f o u r d i f f e r e n t$ $d i g i t s i s f o r m e d b y u s i n g t h e$ $d i g i t s 1, 2, 3, 4, 5, 6, 7, i n a l l p o s s i b l e$ $w a y s e a c h d i g i t o c c u r i n g o n c e$ $o n l y . f i n d h o w m a n y o f t h e m a r e$ $g r e a t e r t h a n 3400$

Question Number 26473 Answers: 1 Comments: 0

How many numbers less than 1000 and divisible by 5 can be formed with the digits 0, 1, 2 ,3 ,4 ,5 6 ,7 ,8 ,9,each digit not occuring more than once in each number?

$H o w m a n y n u m b e r s l e s s t h a n$ $1000 a n d d i v i s i b l e b y 5 c a n b e$ $f o r m e d w i t h t h e d i g i t s 0, 1, 2, 3, 4, 5$ $6, 7, 8, 9, e a c h d i g i t n o t o c c u r i n g$ $m o r e t h a n o n c e i n e a c h n u m b e r ?$

Question Number 25929 Answers: 0 Comments: 0

Show that the coefficients of x^m and x^n in (1+x)^(m+n) are equal.

$Show that the coefficients of x^{m} and x^{n} in {(1 + x)}^{m + n} are equal .$

Question Number 25928 Answers: 0 Comments: 0

Expand (1−x)^4 .Hence,find S if S=(1−x^3 )^4 −4(1−x^3 )^3 +6(1−x^3 )^2 −4(1−x^3 )^ +1.

$Expand {(1 - x)}^{4} . H ence, find S if S = {(1 - x^{3})}^{4} - 4 {(1 - x^{3})}^{3} + 6 {(1 - x^{3})}^{2} - 4 {(1 - x^{3})}^{} + 1 .$

Question Number 25314 Answers: 1 Comments: 1

prove that 0!=1

$p r o v e t h a t 0! = 1$

Question Number 25237 Answers: 0 Comments: 1

prooove that 0!=1

$p r o o o v e t h a t 0! = 1$

Question Number 22820 Answers: 0 Comments: 2

total number of permutations of five abjects → A,A,A,B,B in a circle?

$t o t a l n u m b e r o f p e r m u t a t i o n s o f$ $f i v e a b j e c t s \to A, A, A, B, B$ $i n a c i r c l e ?$

Question Number 22435 Answers: 0 Comments: 0

C_0 ^(2n) C_n −C_1 ^(2n−2) C_n +C_2 ^(2n−4) C_n .... equals to

$C_{0}^{2 n} C_{n} - C_{1}^{2 n - 2} C_{n} + C_{2}^{2 n - 4} C_{n} . . . .$ $equals to$

Question Number 22128 Answers: 0 Comments: 2

Question Number 22044 Answers: 1 Comments: 0

Let A = {1, 2, 3, ....., n}, if a_i is the minimum element of the set A; (where A; denotes the subset of A containing exactly three elements) and X denotes the set of A_i ′s, then evaluate Σ_(A_i ∈X) a.

$Let A = {1, 2, 3, . . . . ., n}, if a_{i} is the$ $minimum element of the set A; (where$ $A; denotes the subset of A containing$ $exactly three elements) and X denotes$ $the set of A_{i}^{'} s, then evaluate \sum_{A_{i} \in X} a .$

Question Number 22043 Answers: 1 Comments: 0

In how many ways we can choose 3 squares on a chess board such that one of the squares has its two sides common to other two squares?

$In how many ways we can choose 3$ $squares on a chess board such that one$ $of the squares has its two sides common$ $to other two squares ?$

Question Number 22042 Answers: 1 Comments: 0

Determine the number of ordered pairs of positive integers (a, b) such that the least common multiple of a and b is 2^3 ∙5^7 ∙11^(13) .

$Determine the number of ordered$ $pairs of positive integers (a, b) such$ $that the least common multiple of a$ $and b is 2^{3} \cdot 5^{7} \cdot 11^{13} .$

Question Number 22041 Answers: 0 Comments: 0

On the modified chess board 10 × 10, Amit and Suresh two persons which start moving towards each other. Each person moving with same constant speed. Amit can move only to the right and upwards along the lines while Suresh can move only to the left or downwards along the lines of the chess boards. The total number of ways in which Amit and Suresh can meet at same point during their trip.

$On the modified chess board 10 \times 10,$ $Amit and Suresh two persons which$ $start moving towards each other . Each$ $person moving with same constant$ $speed . Amit can move only to the$ $right and upwards along the lines$ $while Suresh can move only to the left$ $or downwards along the lines of the$ $chess boards . The total number of$ $ways in which Amit and Suresh can$ $meet at same point during their trip .$

Question Number 22040 Answers: 0 Comments: 4

The total number of non-similar triangles which can be formed such that all the angles of the triangle are integers is

$The total number of non - similar$ $triangles which can be formed such$ $that all the angles of the triangle are$ $integers is$

Question Number 22038 Answers: 0 Comments: 1

The symbols +, +, ×, ×, ★, •, are placed in the squares of the adjoining figure. The number of ways of placing symbols so that no row remains empty is

$The symbols +, +, \times, \times, ★, ∙, are$ $placed in the squares of the adjoining$ $figure . The number of ways of placing$ $symbols so that no row remains empty$ $is$

Question Number 22037 Answers: 0 Comments: 2

How many 5-digit numbers from the digits {0, 1, ....., 9} have? (i) Strictly increasing digits (ii) Strictly increasing or decreasing digits (iii) Increasing digits (iv) Increasing or decreasing digits

$How many 5 - digit numbers from the$ $digits {0, 1, . . . . ., 9} have ?$ $(i) Strictly increasing digits$ $(ii) Strictly increasing or decreasing$ $digits$ $(iii) Increasing digits$ $(iv) Increasing or decreasing digits$

Question Number 22036 Answers: 0 Comments: 1

2n objects of each of three kinds are given to two persons, so that each person gets 3n objects. Prove that this can be done in 3n^2 + 3n + 1 ways.

$2 n objects of each of three kinds are$ $given to two persons, so that each$ $person gets 3 n objects . Prove that$ $this can be done in 3 n^{2} + 3 n + 1 ways .$

Question Number 22035 Answers: 0 Comments: 0

The number of five digits can be made with the digits 1, 2, 3 each of which can be used atmost thrice in a number is

$The number of five digits can be made$ $with the digits 1, 2, 3 each of which can$ $be used atmost thrice in a number is$

Question Number 21977 Answers: 1 Comments: 8

Let n be the number of ways in which 5 boys and 5 girls stand in a queue in such a way that all the girls stand consecutively in the queue. Let m be the number of ways in which 5 boys and 5 girls can stand in a queue in such a way that exactly four girls stand consecutively in the queue. Then the value of (m/n) is

$Let n be the number of ways in which$ $5 boys and 5 girls stand in a queue in$ $such a way that all the girls stand$ $consecutively in the queue . Let m be$ $the number of ways in which 5 boys$ $and 5 girls can stand in a queue in such$ $a way that exactly four girls stand$ $consecutively in the queue . Then the$ $value of \frac{m}{n} is$

Question Number 21933 Answers: 0 Comments: 11

Let n_1 < n_2 < n_3 < n_4 < n_5 be positive integers such that n_1 + n_2 + n_3 + n_4 + n_5 = 20. Then the number of such distinct arrangements (n_1 , n_2 , n_3 , n_4 , n_5 ) is

$Let n_{1} < n_{2} < n_{3} < n_{4} < n_{5} be positive$ $integers such that n_{1} + n_{2} + n_{3} + n_{4} +$ $n_{5} = 20 . Then the number of such$ $distinct arrangements (n_{1}, n_{2}, n_{3}, n_{4}, n_{5})$ $is$

Question Number 21931 Answers: 0 Comments: 2

The number of ways of distributing six identical mathematics books and six identical physics books among three students such that each student gets atleast one mathematics book and atleast one physics book is ((5.5!)/k), then k is

$The number of ways of distributing six$ $identical mathematics books and six$ $identical physics books among three$ $students such that each student gets$ $atleast one mathematics book and$ $atleast one physics book is \frac{5.5!}{k}, then k$ $is$

Question Number 21930 Answers: 0 Comments: 3

An eight digit number is formed from 1, 2, 3, 4 such that product of all digits is always 3072, the total number of ways is (23.^8 C_k ), where the value of k is

$An eight digit number is formed from$ $1, 2, 3, 4 such that product of all digits$ $is always 3072, the total number of$ $ways is (23 .^{8} C_{k}), where the value of k$ $is$

Question Number 21929 Answers: 0 Comments: 2

There are 8 Hindi novels and 6 English novels. 4 Hindi novels and 3 English novels are selected and arranged in a row such that they are alternate then no. of ways is

$There are 8 Hindi novels and 6 English$ $novels . 4 Hindi novels and 3 English$ $novels are selected and arranged in a$ $row such that they are alternate then$ $no . of ways is$

Question Number 21917 Answers: 0 Comments: 4

How many seven letter words can be formed by using the letters of the word SUCCESS so that neither two C nor two S are together?

$How many seven letter words can be$ $formed by using the letters of the word$ $SUCCESS so that neither two C nor$ $two S are together ?$

Question Number 21913 Answers: 0 Comments: 0

Let a_n denote the number of all n-digit positive integers formed by the digits 0, 1 or both such that no consecutive digits in them are 0. Let b_n = the number of such n-digit integers ending with digit 1 and c_n = the number of such n-digit integers ending with digit 0. 1. Which of the following is correct? (1) a_(17) = a_(16) + a_(15) (2) c_(17) ≠ c_(16) + c_(15) (3) b_(17) ≠ b_(16) + c_(16) (4) a_(17) = c_(17) + b_(16) 2. The value of b_6 is

$Let a_{n} denote the number of all n - digit$ $positive integers formed by the digits$ $0, 1 or both such that no consecutive$ $digits in them are 0 . Let b_{n} = the$ $number of such n - digit integers ending$ $with digit 1 and c_{n} = the number of$ $such n - digit integers ending with$ $digit 0 .$ $1 . Which of the following is correct ?$ $(1) a_{17} = a_{16} + a_{15}$ $(2) c_{17} \neq c_{16} + c_{15}$ $(3) b_{17} \neq b_{16} + c_{16}$ $(4) a_{17} = c_{17} + b_{16}$ $2 . The value of b_{6} is$

Question Number 21813 Answers: 0 Comments: 0

x_1 +x_2 +x_3 =5 ways=5−1C_(3−1) =4C_2 =6

$x_{1} + x_{2} + x_{3} = 5$ $w a y s = 5 - 1 C_{3 - 1} = 4 C_{2} = 6$

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