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=[tex]\frac{7!}{2!2!}[/tex]
PAEAI
Total number of ways in which PAEAI can arranged=[tex]\frac{5!}{2!}[/tex]
Total number of arrangements when all consonant appear together=[tex]\frac{7!}{2!2!}\times \frac{5!}{2!}[/tex]
Total number of arrangements when all consonant appear together=[tex]\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[/tex]
By using formula ;[tex]n!=n(n-1)(n-2)...2\times 1[/tex]
