Multiple choice

If the letters of the word (\"MISSISSIPPI\") are written down at random, in a row the probability that no two 'S' occur together is:

  1. 5/33

  2. 7/33

  3. 6/31

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total letters = 11 (M:1, I:4, S:4, P:2). Total arrangements = 11!/(4!4!2!). Arrangements with no two S together: place other 7 letters (M,I,I,I,I,P,P) in 7!/(4!2!) ways. There are 8 gaps to place 4 S's: 8C4. Probability = (8C4 * 7!/(4!2!)) / (11!/(4!4!2!)) = 7/33.

AI explanation

The total number of arrangements is 11 factorial divided by the factorials of 4, 4, and 2, which equals 34650. To find the arrangements where no two 'S' letters are together, first arrange the remaining 7 letters (M, I, I, I, I, P, P) in 7 factorial divided by the factorials of 4 and 2 ways, giving 105 arrangements. These 7 letters create 8 gaps where the 4 'S' letters can be placed, which is done in 8 choose 4 ways, equal to 70. The favorable arrangements equal 105 times 70, which is 7350, and dividing by 34650 gives a probability of 7/33.

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