how many selection of four letters can be made from word 'proportion'.(dont solve by mutinomial theorm)

Dear Rakesh

PP, RR, OOO, T, I, N 

take cases

1. 3 same + 1 different --> 3 same can be from o only and one different from 5 other type of letter= 5 selections

2. 2 same of one kind + 2 same of other kind ----> PPRR, PPOO, OORR = 3 selections

3. 2 same+2different ---> 2 same can be selected from PP,RR,OOO and 2 different from rest five type of letters

                                     = 3C1 x 5C2=30

4. All different letters -----> there are 6 type of letters = 6C4= 15

Total no of selections= 5+3+30+15=53

Please note that you dont have to arrange here you have to just select the possible combination.

All the best.                                                           

AKASH GOYAL

AskiitiansExpert-IIT Delhi

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