The number of numbers of four different digits that can be formed from the digits of the number 12356 such that the numbers are divisible by 4, is
A.
36
B.
48
C.
12
D.
24
Answer :
36
Solution :
\[ \times \times \left| {\begin{array}{*{20}{c}}
{1,3,5} \\
\times
\end{array}} \right.\left| {\begin{array}{*{20}{c}}
{2,6} \\
\times
\end{array}} \right.\]
The units place can be filled in 2 ways.
The tens place can be filled in 3 ways.
The remaining two places can be filled by any two of the remaining three digits. So, the required number of numbers $$ = 2 \times 3 \times {\,^3}{P_2}.$$
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