How many distinct permutations can be made from the letters

hawwend8u

hawwend8u

Answered question

2022-05-21

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

Answer & Explanation

Arabella Alvarez

Arabella Alvarez

Beginner2022-05-22Added 8 answers

Step 1
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 + ... = n . .
Then, no. of possible distinct permutations is given by n ! ( r 1 ! ) ( r 2 ! ) ( r 3 ! ) ...
Step 2
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 ! )
= 8 × 7 × 6 × 5 × 4 2 ! = 3360 .

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