Question

how many words can be formed by taking four different letters of mathematics​

Answer 1

Answer:

The four letter word can be formed in the following ways. (all distinct letters),(two letters same of one kind and other two distinct),(four letters same of two different kind) case 1:All distinct letter We have 8 distinct letters(M,A,T,H,E,I,C,Ssee

Answer 2

Answer:

Step-by-step explanation:

There are 8 distinct letters: M-A-T-H-E-I-C-S. 3 letters M, A, and T are represented twice (double letter).

Selected 4 letters can have following 3 patterns:

1. abcd - all 4 letters are different:

(choosing 4 distinct letters out of 8, when order matters) or (choosing 4 distinct letters out of 8 when order does not matter and multiplying by 4! to get different arrangement of these 4 distinct letters);

2. aabb - from 4 letters 2 are the same and other 2 are also the same:

- 3C2 choosing which two double letter will provide two letters (out of 3 double letter - MAT), multiplying by to get different arrangements (for example MMAA can be arranged in # of ways);

3. aabc - from 4 letters 2 are the same and other 2 are different:

- 3C1 choosing which letter will proved with 2 letters (out of 3 double letter - MAT), 7C2 choosing third and fourth letters out of 7 distinct letters left and multiplying by to get different arrangements (for example MMIC can be arranged in # of ways).

1680+18+756=2454

Answer: 2454.