Question

The number of permutations of $n$ distinct objects taken $r$ together in which include $3$ particular things must occur together

• A. ${}^{n-3}{C}_{r-3}(r-2)!\times 3!$
• B. ${}^n{C}_{r-3}\times 3!$
• C. ${}^{n-3}{p}_{r-3}\times 3!$
• D. $P_3{\times }^{n-3}{P}_{r-3}$

Answer 1

Answer: (A)

${}^{n-3}{C}_{r-3}(r-2)!\times 3!$

Number of ways of selection of (r-3) objects out of (n-3) objects

${=}^{n-3}{C}_{r-3}$

When we bundle 3 things together,

$no.ofobjects=(r-3)+1$

$=(r-2)$

which can be arranged in (r-2)! ways also 3 objects

in the bundle can be arranged among themselves in 3! ways

$\therefore Permutation{=}^{n-3}{C}_{r-3}(r-2)!3!$