In how many ways can 4 letters be selected from the word WHITEHAT? In the solution, 4 cases were given. Case 1:no repetition ie 6c2=15 case2: 2 H present= 5C2=10 case3: 2 T present= 5C2=10 case4: HH & TT=1 Won't there be a 5th case where there is exactly one H and one T and rest 2 is selected from W, E, A, I?

Hi, so please correct me if i'm wrong! because you didn't mention the correct answer. I could come up with 3 cases 1st case: all are different . we have 2H,2T,W,I,E,A ie, 6 letters in total so first case where all are different , you can do it in 6C4 ways . 2nd case: where 2 are similar and 2 are different- 2C1*5C2 2C1 - selecting either H OR T 5C2- selecting 2 different letters from the 5 letters available after selecting the 2 similar ones. case 3: all are similar which will be only ONE case because H AND T are the only letters which are repeating .