Class 11

Math

Algebra

Permutations and Combinations

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

- $2425 (25_{25}−25_{15})$
- $2425 (25_{25}−25_{10})$
- $2425 (25_{25}+25_{15})$
- $2425 (25_{25}+25_{10})$

$=25_{16}$

No of permutations of 17 objects

$=25_{17}$

18 $→25_{18}$

19 $→25_{19}$

25 $→25_{25}$

So, S $=$ $25_{25}+25_{24}+................+25_{16}$

$=$ $25−125_{16}[25_{10}−1] $

$⇒$ Ans $=$ $2425 (25_{25}−25_{15})$