# How many distinct permutations can be made from the letters of the word "infinity"?

Jan 25, 2017

$\text{The Reqd. No. of Permutations=} 3360.$

#### Explanation:

Suppose that, out of $n$ things, ${r}_{1}$ are of first type, ${r}_{2}$ are of

second type, ${r}_{3}$ are of third type,..., where ${r}_{1} + {r}_{2} + {r}_{3} + \ldots = n .$

Then, no. of possible distinct permutations is given by

(n!)/{(r_1!)(r_2!)(r_3!)...}

In our Example, there are total $8$ letters in the word INFINITY ,

out of which, $3$ letters are of one type (i.e., the letter I ), $2$

are of second type (i.e., the letter N ) and the remaining $3$ are

(i.e., the letters F,T and Y) are each of $1$ type.

Thus, $n = 8 , {r}_{1} = 3 , {r}_{2} = 2 , {r}_{3} = {r}_{4} = {r}_{5} = 1$.

"The Reqd. No. of Permutations="(8!)/{(3!)(2!)(1!)(1!)(1!)}

=(8xx7xx6xx5xx4)/(2!)=3360.

Enjoy Maths.!