Question

In how many ways can the letters in the word MATHEMATICS be reshuffled so that all consonants appear together?

Answer 1

Answer:

75600

Step-by-step explanation:

We are given that  a word MATHEMATICS

Total letters =11

M repeated 2 times

T repeated 2 times

A repeated 2 times

Total vowels=4

Let MTHMTCS=P

Total number of ways in which MTHMTCS can be arranged=$\frac{7!}{2!2!}$

PAEAI

Total number of ways in which PAEAI can arranged=$\frac{5!}{2!}$

Total number of arrangements when all consonant appear together=$\frac{7!}{2!2!}\times \frac{5!}{2!}$

Total number of arrangements when all consonant appear together=$\frac{7!5!}{2\times 2\times 2}=\frac{7\times 6\times 5\times 4\times 3\times 2\times 1\times 5\times 4\times 3\times 2\times 1}{8}=75600$

By using formula ;$n!=n(n-1)(n-2)...2\times 1$