The number of 6-digit numbers that can be made with the digits 1, 2, 3 and 4 and having exactly two pairs of digits is
A.
480
B.
540
C.
1080
D.
None of these
Answer :
1080
Solution :
The number will have 2 pairs and 2 different digits.
The number of selections $$ = {\,^4}{C_2} \times {\,^2}{C_2},$$ and for each selection, number of arrangements $$ = \frac{{6!}}{{2!\,2!}}.$$ Therefore, the required number of numbers $$ = {\,^4}{C_2} \times {\,^2}{C_2} \times \frac{{6!}}{{2!\,2!}}.$$
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