Question:medium

The number of permutations of the letters of the word INSTITUTION are .......

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Divide n factorial by the factorials of the repeated letters.
Updated On: Oct 1, 2026
  • \(6652800\)
  • \(221760\)
  • \(1108800\)
  • \(554400\)
Show Solution

The Correct Option is D

Solution and Explanation

Step 1: Approach
Place the repeated letters one kind at a time using combinations.

Step 2: Choose positions
From 11 places choose 2 for I: $\binom{11}{2}=55$. From the remaining 9 choose 3 for N: $\binom{9}{3}=84$. From the remaining 6 choose 3 for T: $\binom{6}{3}=20$.

Step 3: Remaining letters
The 3 spaces left are filled by S, U, O in $3!=6$ ways.

Step 4: Total
\[ 55\times84\times20\times6=554400 \]
This is option (D).

Final Answer:
The word has 11 letters with I twice, N three times and T three times, giving 554400 arrangements, option (D). \[ \boxed{554400} \]
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