Problem Solving : Permutation and combination Problem 1 : In how many ways can the letter of the word PROPORTION be arranged by taking 4 letters at a time?
In how many ways can the letter of the word PROPORTION be arranged by taking 4 letters at a time? Solution: P R O P O R T I O N below I've wrote letters without repeated words and then how many times particular word repeated P R O T I N P R O O Here (P, P) 2 P, (R, R) 2 R, and (O,O,O) 3 O from the question here we gonna select 4 words hence we have the following chance to select those 4 words Chance 1: 3 O and remaining 1 are different (That means (O,O,O)--> 3 word and (P,R,T,I,N) ---> 1 word from the 5) Chance 2: two of same words and other two of the same words (here (O,O,O), (T,T) and (P,P) out of 3 pairs we gonna select 2 pair of words ) Chance 3: Two of same words and other two are different words (here (O,O,O), (T,T) and (P,P) out of 3 pairs we gonna select 1 pair of word and other 2 word from (R, O, I, N, T) words consider P,P has been selected pair ) Chance 4: All 4 are different ( here P, R, ...