1.

Find the number of permutations of n different things taken r at a time such that two specific things occur together.

Answer»

A bundle of 2 specific things can be put in r places in (r – 1) ways (Why?) and 2 things in the bundle can be arranged themselves into 2! ways. Now (n – 2) things will be arranged in (r – 2) places in n –2Pr –2 ways.

Thus, using the fundamental principle of counting, the required numer of permutations will be 2!.(r - 1).n-2Pr-2



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