If $$3n$$ different things can be equally distributed among $$3$$ persons in $$k$$
ways then the number of ways to divide the $$3n$$ things in $$3$$ equal groups is
A.
$$k \times 3!$$
B.
$$\frac{k}{{3!}}$$
C.
$${\left( {3!} \right)^k}$$
D.
None of these
Answer :
$$\frac{k}{{3!}}$$
Solution :
(The number of ways of dividing in 3 equal groups) $$ \times \left( {3!} \right)$$
= the number of ways to distribute equally among 3 persons.
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