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

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


1 Answers

AKASH GOYAL AskiitiansExpert-IITD
419 Points
10 years ago

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.                                                           


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