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?

Question

Answer 1

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 .

Answer 2

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 .

Answer 3

That case is already covered in the 6c2 cases in which all them are different

Answer 4

That case is already covered in the 6c2 cases in which all them are different

Answer 5

i think they made different cases for H and T

Answer 6

i think they made different cases for H and T

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