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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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