Question

The number of ways in which $20$ volunteers can be divided into groups of $4,7$ and $9$ persons is-

• A. ${{}^{16}C}_7\times {{}^{16}C}_2$
• B. ${{}^{20}C}_7\times {{}^{11}C}_4$
• C. ${{}^{20}C}_4\times {{}^{16}C}_7$
• D. ${{}^{20}C}_9\times {{}^{13}C}_9$

Answer 1

Answer: (C)

${{}^{20}C}_4\times {{}^{16}C}_7$

For unequal group distrubution

$k=p+q+r$

$20=4+7+9$

So, first of all take $4$ volunteer out of $20$ and then take $7$ out of remaining volunteers and so on.

No. of ways of making group ${=}^{20}{C}_4{.}^{16}{C}_7{.}^9{C}_9$

${=}^{20}{C}_4{.}^{16}{C}_7$

Hence, the option are not correct