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

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Answer 1 · 2017-01-25T14:47:14

#"The Reqd. No. of Permutations="3360.#

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!)...}#

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.!