The number of ways in which 6 different balls can be put in two boxes of different sizes so that no box remains empty is
A.
62
B.
64
C.
36
D.
None of these
Answer :
62
Solution :
Each ball can be put in 2 ways (either in one box or the other).
∴ 6 balls can be put in $$2 \times 2 \times .....$$ to six times, i.e., $${2^6}$$ ways. But in two of the ways one box is empty. So, the required number of ways $$ = {2^6} - 2.$$
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