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Permutation: n Different Things Taken r at a Time

There are p i...

Question

There are p intermediate stations on a railway line from Delhi to Amritsar. In how many way can a super-fast train stop at three of these intermediate stations if no two of them are to be consecutive?

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Solution

$(p - 3)$ non-stopping. There will be $(p - 3) + 1 = p - 2$ gaps where three stopping stations could be located.
$∴^{p - 2} C_{3}$ ways.

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Permutation: n Different Things Taken r at a Time

Standard XII Mathematics

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