Q56 / 150 · MHT CET 2026 (20 April Shift 2) · Mathematics
The number of permutations of the letters of the word INSTITUTION are .......
- A$6652800$
- B$221760$
- C$1108800$
- Correct answerD$554400$
Solution
The word INSTITUTION has $11$ letters.
The frequencies of the letters are:
I appears $3$ times.
N appears $2$ times.
T appears $3$ times.
S, U, O appear $1$ time each.
The total number of permutations is given by $\dfrac{11!}{3! \times 2! \times 3!}$.
$\dfrac{11!}{3! \times 2! \times 3!} = \dfrac{39916800}{6 \times 2 \times 6} = \dfrac{39916800}{72} = 554400$
Answer: $554400$
The frequencies of the letters are:
I appears $3$ times.
N appears $2$ times.
T appears $3$ times.
S, U, O appear $1$ time each.
The total number of permutations is given by $\dfrac{11!}{3! \times 2! \times 3!}$.
$\dfrac{11!}{3! \times 2! \times 3!} = \dfrac{39916800}{6 \times 2 \times 6} = \dfrac{39916800}{72} = 554400$
Answer: $554400$
Hence, the correct answer is option: 'D'.