Find thr number of permutation of the letter MATHEMATICS
Answers
the first consonant is M or T and A,(T/M) are repeated :
2×10!2!2!=10!2!
If the first consonant is C,H or S and A,T,M are repeated:
3×10!2!2!2!
Thus total amount equals:
10!2!+3×10!2!2!2!=2!2!10!+3×10!2!2!2!=4×10!+3×10!8=7×10!8
We can ensure this result with a reversal case. Choosing a vocal as the first letter, total amount of choices is:
10!2!2!+2×10!2!2!2!=10!2!=4×10!8
Thus total amount of combinations starting with either consonant or vocal is
7×10!8+4×10!8=11!2!2!2!=(112,2,2)
which equals every permutation of the word, when duplicate letters are concerned.
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Answer:
Total alphabets in MATHEMATICS = 11
Total cases without taking repetition = 11 x 11
Cases of repetition = 11
Number of permutations in word MATHEMATICS=
= 11 x 11 - 11
= 110 - 11
= 99 CASES