Question

No. of permutations of $25$ dissimilar things taken more than $15$ at a time when repetitions are allowed is

• A. $\frac{25}{24}({25}^{25}-{25}^{15})$
• B. $\frac{25}{24}({25}^{25}-{25}^{10})$
• C. $\frac{25}{24}({25}^{25}+{25}^{15})$
• D. $\frac{25}{24}({25}^{25}+{25}^{10})$

Answer 1

Answer: (A)

$\frac{25}{24}({25}^{25}-{25}^{15})$

No of permutations of 16 objects $={25}^{16}$
No of permutations of 17 objects $={25}^{17}$
18 $\to {25}^{18}$
19 $\to {25}^{19}$
25 $\to {25}^{25}$
So, S $=$ ${25}^{25}+{25}^{24}+................+{25}^{16}$
$=$ $\frac{{25}^{16}[{25}^{10}-1]}{25-1}$
$\Rightarrow$ Ans $=$ $\frac{25}{24}({25}^{25}-{25}^{15})$