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Permutation and CombinationQuestion and Answers: Page 23
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Question and Answers Forum |
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Permutation and CombinationQuestion and Answers: Page 23 |
| x_1 +x_2 +x_3 =5 ways=5−1C_(3−1) =4C_2 =6 |
| Five balls are to be placed in three boxes. Each can hold all the five balls. In how many different ways can we place the balls so that no box remains empty, if balls are different but boxes are identical? |
| There are n straight lines in a plane, no two of which are parallel and no three pass through the same point. Their point of intersection are joined. Then the number of fresh lines thus obtained is |
| The number of integers which lie between 1 and 10^6 and which have sum of digits equal to 12 is |
| There are n white and n red balls marked 1, 2, 3, ....n. The number of ways we can arrange these balls in a row so that neighbouring balls are of different colours is |
| The result of 11 chess matches (as win, lose or draw) are to be forecast. Out of all possible forecasts, the number of ways in which 8 correct and 3 incorrect results can be forecast is |
| Six cards and six envelopes are numbered 1, 2, 3, 4, 5, 6 and cards are to be placed in envelopes so that each envelope contains exactly one card and no card is placed in the envelope bearing the same number and moreover the card numbered 1 is always placed in envelope numbered 2. Then the number of ways it can be done is |
| There are 3 apartments A, B and C for rent in a building. Each apartment will accept either 3 or 4 occupants. The number of ways of renting the apartments to 10 students |
| There are m points on the line AB and n points on the line AC, excluding the point A. Triangles are formed joining these points (i) When point A is not included, (ii) When point A is included. The ratio of the number of such triangles is |
| I have 6 friends and during a vacation I met them during several dinners. I found that I dined with all the 6 exactly on 1 day; with every 5 of them on 2 days; with every 4 of them on 3 days; with every 3 of them on 4 days; with every 2 of them on 5 days. Further every friend was present at 7 dinners and every friend was absent at 7 dinners. How many dinners did I have alone? |
| In a group of ten persons, each person is asked to write the sum of the ages of all the other 9 persons. If all the ten sums form the 9-element set {82, 83, 84, 85, 87, 90, 91, 92} find the individual ages of the persons (assuming them to be whole numbers of years). |
| Suppose A_1 A_2 ...A_(20) is a 20-sided regular polygon. How many non-isosceles (scalene) triangles can be formed whose vertices are among the vertices of the polygon but whose sides are not the sides of the polygon? |
| How many four-digit numbers are there whose decimal notation contains not more than two distinct digits? |
| How many six-digit numbers contain exactly four different digits? |
| Prove that ((n^2 !)/((n!)^n )) is an integer, n ∈ N. |
| If n objects are arranged in a row, then find the number of ways of selecting three of these objects so that no two of them are next to each other. |
| Determine the largest 3-digit prime factor of the integer^(2000) C_(1000) . |
| Find the number of ways in which n distinct balls can be put into three boxes so that no two boxes remain empty. |
| Four dice are rolled. The number of ways in which at least one die shows 3, is |
| Prove that (6n)! is divisible by 2^(2n) .3^n . |
| In how many ways can the letters of the word PATLIPUTRA be arranged, so that the relative order of vowels are consonants do not alter? |
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| Find the number of ways the digits 0,1,2 and 3 can be permuted to give rise to a number greater than 2000. |
| In how many ways can a family of 5 brothers be seated round a table if (i) 2 brothers must seat next to each other. (ii) 2 brothers must not seat together. |
| In how many ways can the letters of the word. EVERMORE be arrange if the word must begin with (i) R (ii) E |
| Find how many number greater than 2,500 can be formed from the digit 0, 1, 2, 3, 4 if no digit can be used more than once. |