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Permutation and CombinationQuestion and Answers: Page 18

Question Number 63246 Answers: 0 Comments: 2

Arrange these digits: 1 1 2 2 3 3 4 4 So that the 1′s are four digit apart So that the 2′s are three digit apart So that the 3′s are two digit apart So that the 4′s are one digit apart

$Arrange these digits : 1 1 2 2 3 3 4 4$ $So that the 1^{'} s are four digit apart$ $So that the 2^{'} s are three digit apart$ $So that the 3^{'} s are two digit apart$ $So that the 4^{'} s are one digit apart$

Question Number 62022 Answers: 1 Comments: 0

Question Number 62014 Answers: 1 Comments: 0

Question Number 61860 Answers: 0 Comments: 0

simplify: ^(n + 1) C_r − ^(n − 1) C_r

$simplify : \overset{n + 1}{} C_{r} - \overset{n - 1}{} C_{r}$

Question Number 61377 Answers: 0 Comments: 0

Find the multinomial coefficient: ((( 9)),((3, 5, 1, 0)) )

$Find the multinomial coefficient : (\begin{matrix} 9 \\ 3, 5, 1, 0 \end{matrix})$

Question Number 59625 Answers: 0 Comments: 0

Sum the series: ((( ^n C_1 )/( ^n C_0 )))^2 + (2 × (( ^n C_2 )/( ^n C_1 ))) + (3 × (( ^n C_3 )/( ^n C_2 )))^2 + .... n terms

$Sum the series : {(\frac{\overset{n}{} C_{1}}{\overset{n}{} C_{0}})}^{2} + (2 \times \frac{\overset{n}{} C_{2}}{\overset{n}{} C_{1}}) + {(3 \times \frac{\overset{n}{} C_{3}}{\overset{n}{} C_{2}})}^{2} + . . . . n terms$

Question Number 59021 Answers: 2 Comments: 10

[Q58885 reposted] How many 4−digit numbers abcd exist which are divisible by 3 and satisfy a≤b≤c≤d?

$[Q 58885 r e p o s t e d]$ $H o w m a n y 4 - d i g i t n u m b e r s a b c d e x i s t$ $w h i c h a r e d i v i s i b l e b y 3 a n d s a t i s f y$ $a ⩽ b ⩽ c ⩽ d ?$

Question Number 58373 Answers: 1 Comments: 1

Find the coefficient of x^6 in (2x + 1)^6 (x^2 + x + (1/4))^4

$Find the coefficient of x^{6} in {(2 x + 1)}^{6} {(x^{2} + x + \frac{1}{4})}^{4}$

Question Number 58049 Answers: 0 Comments: 0

Question Number 57985 Answers: 2 Comments: 0

Find the number of integer solutions for a×b×c×d=18900 with a,b,c,d≥1.

$F i n d t h e n u m b e r o f i n t e g e r s o l u t i o n s$ $f o r a \times b \times c \times d = 18900$ $w i t h a, b, c, d ⩾ 1 .$

Question Number 57909 Answers: 2 Comments: 0

n men and n women should be arranged alternately in a row, how many ways can this be done? if the same should be done on a table, how many ways then?

$n m e n a n d n w o m e n s h o u l d b e a r r a n g e d$ $a l t e r n a t e l y i n a r o w, h o w m a n y w a y s$ $c a n t h i s b e d o n e ? i f t h e s a m e s h o u l d$ $b e d o n e o n a t a b l e, h o w m a n y w a y s t h e n ?$

Question Number 57688 Answers: 1 Comments: 12

Solve for n: Σ_i ^(n − 1) ^n C_i 2^i = 65, n ∈ Z^+ . where zero is included

$Solve for n : \underset{i}{\sum^{n - 1}} \overset{n}{} C_{i} 2^{i} = 65, n \in Z^{+} . where zero is$ $included$

Question Number 57363 Answers: 0 Comments: 3

Question Number 57336 Answers: 2 Comments: 0

If n be even, show that the expression ((n(n + 2)(n + 4) ... (2n − 2))/(1.3.5 ... (n − 1))) simplify to 2^(n − 1)

$If n be even, show that the expression \frac{n (n + 2) (n + 4) . . . (2 n - 2)}{1.3.5 . . . (n - 1)}$ $simplify to 2^{n - 1}$

Question Number 57048 Answers: 2 Comments: 1

Question Number 57046 Answers: 0 Comments: 1

Question Number 57042 Answers: 1 Comments: 1

Question Number 56961 Answers: 1 Comments: 0

Out of 6 mathematicians and 7 physicists a committee consisting of 3 mathematicians and 3 physicists is to be formed. In how many ways can this be done if two particular mathematicians cannot be on the commitee?

$Out of 6 mathematicians and 7 physicists$ $a committee consisting of 3 mathematicians$ $and 3 physicists is to be formed . In how$ $many ways can this be done if two$ $particular mathematicians cannot be$ $on the commitee ?$

Question Number 56913 Answers: 1 Comments: 2

How many possible solution sets that satisfy x_1 + x_2 + x_3 + x_4 = 5 with 0 ≤ x_1 ≤ 3 0 ≤ x_2 ≤ 3 0 ≤ x_3 ≤ 2 0 ≤ x_4 ≤ 2

$How many possible solution sets that satisfy$ $x_{1} + x_{2} + x_{3} + x_{4} = 5$ $with$ $0 ⩽ x_{1} ⩽ 3$ $0 ⩽ x_{2} ⩽ 3$ $0 ⩽ x_{3} ⩽ 2$ $0 ⩽ x_{4} ⩽ 2$

Question Number 56820 Answers: 0 Comments: 0

the no of traingle formed by the vertices of a decagon such that atleast one side is in common

$the no of traingle formed by the vertices$ $of a decagon such that atleast one side$ $is in common$

Question Number 56784 Answers: 0 Comments: 0

Question Number 56743 Answers: 1 Comments: 0

Question Number 56688 Answers: 1 Comments: 0

How many odd numbers, greater than 60000, can be made from the digits 5,6,7,8,9,0, if no number contains any digit more than ones?

$How many odd numbers, greater than$ $60000, can be made from the digits$ $5, 6, 7, 8, 9, 0, if no number contains any$ $digit more than ones ?$

Question Number 56678 Answers: 1 Comments: 0

A box contains 9 whites, 7 red and 4 blue balls. Three balls are picked at random, one after the other without replacement. a) find the probability that: i. they are all of the same color ii. there is one of each colour iii. two of them are red b) if it is known that the first one picked is blue, find the probability that the rest are white.

$A box contains 9 whites, 7 red and 4 blue$ $balls . Three balls are picked at random,$ $one after the other without replacement .$ $a) find the probability that :$ $i . they are all of the same color$ $ii . there is one of each colour$ $iii . two of them are red$ $b) if it is known that the first one picked$ $is blue, find the probability that the rest$ $are white .$

Question Number 56624 Answers: 0 Comments: 2

How many numbers greater than 2000 can be formed using the digits 1,3,4,5,6? how many of these will be even? repetition not allowed.

$How many numbers greater than 2000$ $can be formed using the digits 1, 3, 4, 5, 6 ?$ $how many of these will be even ?$ $repetition not allowed .$

Question Number 56615 Answers: 0 Comments: 4

In how many different ways can the letters of the word OKINKWO be arranged? In how many of these arrangements does an O occupy both end points of the word?

$In how many different ways can the$ $letters of the word OKINKWO be arranged ?$ $In how many of these arrangements$ $does an O occupy both end points of$ $the word ?$

Pg 13 Pg 14 Pg 15 Pg 16 Pg 17 Pg 18 Pg 19 Pg 20 Pg 21 Pg 22

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