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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
The number of words that can be formed by using
the letters of the word 'MATHEMATICS' that start as
well as end with T is
Solution
Letters and frequencies:$M=2,\ A=2,\ T=2,\ H=1,\ E=1,\ I=1,\ C=1,\ S=1$ (total $11$ letters)
Condition: Starts with T and ends with T
Fix $T$ at first and last position.
Remaining letters = $9$ letters:
$M=2,\ A=2,\ H=1,\ E=1,\ I=1,\ C=1,\ S=1$
Number of distinct arrangements of these $9$ letters:
Using division method
$\displaystyle \frac{9!}{2!,2!}$
Final answer:
${\frac{9!}{2!,2!} = 90720}$
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