Question 21 of 42intermediate🔧 ApplyNumerical3 marks

In how many of the distinct permutations of the letters in MISSISSIPPI do the four I's not come together?

Correct Answer

33810

Exercise: EXERCISE 6.3 | Q: 10 | (Page 15)
For More Understanding

Explanation

This is a permutation problem with repeated letters. The word MISSISSIPPI has 11 letters total: M(1), I(4), S(4), P(2). To find permutations where I's do NOT come together, we use the subtraction method: Total permutations minus permutations where all I's are together.

Solution Steps

  1. Step 1: Find total distinct permutations of MISSISSIPPI. Total letters = 11, with I repeated 4 times, S repeated 4 times, P repeated 2 times. Total permutations = 11!/(4!×4!×2!) = 39916800/(24×2424 \times 24×2) = 34650.

  2. Step 2: Find permutations where all four I's come together. Treat four I's as one unit. Now we have 8 units (M, IIII, S, S, S, S, P, P) with S repeated 4 times and P repeated 2 times. Permutations with I's together = 8!/(4!×2!) = 40320/(24×224 \times 2) = 840.

  3. Step 3: Find permutations where I's do NOT come together. Required number = Total permutations - Permutations with I's together = 34650 - 840 = 33810.

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