The number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty is
A.
$$^8{C_3}$$
B.
21
C.
$${3^8}$$
D.
5
Answer :
21
Solution :
We know that the number of ways of distributing $$n$$ identical items among $$r$$ persons, when each one of them receives at least one item is $$^{n - 1}{C_{r - 1}}$$
∴ The required number of ways
$${ = ^{8 - 1}}{C_{3 - 1}} = {\,^7}{C_2} = \frac{{7!}}{{2!5!}} = \frac{{7 \times 6}}{{2 \times 1}} = 21$$
Releted MCQ Question on Algebra >> Permutation and Combination
Releted Question 1
$$^n{C_{r - 1}} = 36,{\,^n}{C_r} = 84$$ and $$^n{C_{r + 1}} = 126,$$ then $$r$$ is:
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated are
Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 ; and then the men select the chairs from amongst the remaining. The number of possible arrangements is