Question

In how many ways the letter ‘solving' can be rearranged to make 7 letter words such that none of the letters repeat?

Answer 1

Heya User,

--> Considering that uh talk about the word "solving" with the letters :->

--> { S , O, L, V , I , N , G } --> No letter repeats itself twice..
--> We use either of 7 letters to fill the first place and remain with the rest 6 letters and 6 positions..
--> We use either of 6 remaining letters to put in the second position and remain with the rest 5 letters and 5 positions..

--> And so on, by Multiplication Principle, we get the no of such words as :-> 7 * 6 * 5 * 4 * 3 * 2 * 1 ---> 7! ---> 5040

--> Just to make sure no word repeats itself, note that the position occupation took place in a unique order..
--> Hence, the answer uh seek for is 5040