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Permutations and Combinations
Permutations with Repetition, Grouping
jee_adv_2026_mock_p1
Grade 12

Question:

The number of ways in which the letters of the word 'MISSISSIPPI' can be arranged such that all I's are together is N. Find N/210.

Step-by-Step Solution

Key Concept: Treat all identical I's as a single unit.
Step 1: Word MISSISSIPPI has: M=1, I=4, S=4, P=2. Step 2: Treat all 4 I's as one unit. Total units = 1 + 1 + 4 + 2 = 8 (M, I-unit, S=4, P=2). Step 3: Arrangements = 8!/(4!2!) = 40320/(24*2) = 840. N = 840. N/210 = 4.
Correct Answer: 4
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