How many different nine digit numbers can be formed from the number 223355888 by rearranging its digits so that the odd digits occupy even positions ?
A.
16
B.
36
C.
60
D.
180
Answer :
60
Solution :
$$X - X - X - X - X.$$ The four digits 3, 3, 5, 5 can be arranged at $$\left( - \right)$$ places in $$\frac{{4!}}{{2!2!}} = 6{\text{ ways}}{\text{.}}$$
The five digits 2, 2, 8, 8, 8 can be arranged at $$\left( X \right)$$ places in $$\frac{{5!}}{{2!3!}}{\text{ ways}} = 10{\text{ ways}}$$
Total no. of arrangements $$ = 6 \times 10 = 60{\text{ ways}}$$
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