In how many ways can the letters in the word MATHEMATICS be reshuffled

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

2 months ago

Solution 1

Guest Guest #2391178
2 months ago

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

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