The total number of 9-digit numbers of different digits is
A.
$$10\left( {9!} \right)$$
B.
$$8\left( {9!} \right)$$
C.
$$9\left( {9!} \right)$$
D.
None of these
Answer :
$$9\left( {9!} \right)$$
Solution :
The first place from the left can be filled in 9 ways (any one except 0).
The other eight places can be filled by the remaining 9 digits in $$^9{P_8}$$ ways.
∴ the number of 9-digit numbers $$ = 9{ \times ^9}\,{P_8}.$$
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