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 = ${}^{6 + 3 - 1}C_{3 - 1} = {}^{8}C_{2} = 28$

More questions

2.
If U = {a, b, c, d, e, f}, A = {a, b, c}, find (U ? A)?.
Options
A. U
B. A
C. ?
D. None of these

3.
Mukul's income is 10% more than Sunil's. How much less is Sunil's income than that of Mukul's?
Options
A. 8.09 %
B. 9.09 %
C. 7.09 %
D. 7.90 %

6. If the number 481 * 673 is completely divisible by 9, then the smallest whole number in place of * will be:
Options
A. 2
B. 5
C. 6
D. 7
E. None of these

8.
The true discount on a certain bill due for nine months at 4 % simple interest is ?150. Find the amount of the bill.
Options
A. ?5150
B. ?5250
C. ?4750
D. ?5650

9.
The present worth of $ 220.50 due in 2 years reckoning compound interest at 5 % is :
Options
A. $ 200
B. $ 197.5
C. $ 202
D. $ 192.25

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