Seat plan changed
A small class of nine boys are to change their seating arrangement by drawing their new seat number from a box. After the seat change, what is the probability that there is only one pair of boys who have switched seats with each other and only three boys who have unchanged seats? If the probability is expressed in terms of , then find .
The answer is 49.
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1 solution
If we assume all permutations of the numbers 0-8, we'd see that there are 9! or 362880 permutations.
Of these 362880 permutations, we would find that 109620 of those permutations have exactly one pair of numbers swapped, 22260 of those have 3 numbers in an unchanged position, and 7560 permutations that satisfy both of those requirements.
7560 / 362880 reduces down to 1 / 48, and 1 + 48 gives us our answer, 49
Nice problem!