Question

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

^{16}C_{7}× ^{13}C_{2}
^{20}C_{7} × ^{11}C_{4}
^{20}C_{4} × ^{16}C_{7}
^{20}C_{9} × ^{13}C_{9}

^{16}C_{7}×^{13}C_{2}^{20}C_{7}×^{11}C_{4}^{20}C_{4}×^{16}C_{7}^{20}C_{9}×^{13}C_{9}Hint:

### Since we have to make groups of 4, 7 , 9 people out of 20 volunteers , find out the number of people that can be selected and similarly those who are selected in one group , they will not participate in other groups.

## The correct answer is: ^{20}C_{4} × ^{16}C_{7}

### We have to make groups of 4, 7 , 9 people out of 20 volunteers

4 people out of 20 can be selected in

7 people out of remaining 16 can be selected in

9 people out of remaining 9 can be selected in

Thus, the number of ways in which 20 volunteers can be divided into groups of 4, 7 and 9 persons is

.

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