Find the number of ways in which 21 balls can be distributed among 3 persons suc

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Question
Find the number of ways in which 21 balls can be distributed among 3 persons such that each person does not receive less than 5 balls.
Options
A. 28
B. 14
C. 21
D. 7

Correct Answer

28

Explanation

Let x, y, z be the number of balls received by the three persons, then

$x ? 5, y ? 5, z ? 5 a n d x + y + z = 21$

Let $u ? 0, v ? 0, w ? 0 t h e n$

$?$ x + y + z =21

$?$ u + 5 + v + 5 + w + 5 = 21

$?$ u + v + w = 6

$?$ Total number of solutions = ${}^{6 + 3 - 1}C_{3 - 1} = {}^{8}C_{2} = 28$

Permutation and Combination problems

Search Results

1. How many four digits numbers greater than 6000 can be made using the digits 0, 4, 2, 6 together with repetition.
Options
A. 64
B. 63
C. 62
D. 60

2. Find the total numbers greater than 4000 that can be formed with digits 2, 3, 4, 5, 6 no digit being repeated in any number ?
Options
A. 120
B. 256
C. 192
D. 244

3. A polygon has 44 diagonals, then the number of its sides are ?
Options
A. 13
B. 9
C. 11
D. 7

4. A decision committee of 5 members is to be formed out of 4 Actors, 3 Directors and 2 Producers. In how many ways a committee of 2 Actors, 2 Directors and 1 Producer can be formed ?
Options
A. 18
B. 24
C. 36
D. 32

5. In how many ways can the letters of the word EDUCATION be rearranged so that the relative position of the vowels and consonants remain the same as in the word EDUCATION?
Options
A. 4! x 4!
B. 5! x 5!
C. 4! x 5!
D. 3! x 4!

7. Four ladies A, B, C and D and four gentlemen E, F, G and H are sitting in a circle round a table facing each other. Directions: (1) No two ladies or two gentlemen are sitting side by side. (2) C, who is sitting between G and E is facing D. (3) F is between D and A and is facing G. (4) H is to the right of B. Question: 1. Who are immediate neighbours of B? 2. E is facing whom?
Options
A. G & H , H
B. F & H , B
C. E & F , F
D. E & H , G

8. In How many ways is it possible to make a selection by taking any number of 15 fruits, namely 3 oranges, 5 apples and 7 mangoes?
Options
A. 131
B. 191
C. 68
D. 3720

9. How many different four letter words can be formed (the words need not be meaningful using the letters of the word "MEDITERRANEAN" such that the first letter is E and the last letter is R?
Options
A. 59
B. 56
C. 64
D. 55

10. There are 7 non-collinear points. How many triangles can be drawn by joining these points?
Options
A. 10
B. 30
C. 35
D. 60

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