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

Question

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

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Aaliyah 2 weeks 2022-01-10T18:41:09+00:00 1 Answer 0 views 0

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    2022-01-10T18:42:40+00:00

    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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45:7+7-4:2-5:5*4+35:2 =? ( )