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Find the number of permutations of `n`distinct things taken `r`together, in which 3 particular things must occur together. |
Answer» Total number of things = n We have to arrange r things out of n in which three things must occur together. Therefore, combination of n things taken r at a time in which3 things always occurs `= ""^(n-3)C_(r-3)` If three things taken together, then it is considered as 1 group. Arrangement of these three things `=3"!"` Now, we have to arrange `= r - 3 + 1 = (r - 2)` objects `therefore" "` Arranged of (r-2) objects `= r - 2"!"` `therefore" "` Total number of arrangements `= ""^(n - 3)C_(r - 3) xx r - 2"!" xx 3"!"` |
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