00:01
Here the total number of students in a group n is given as 9.
00:07
So out of this 9, 6 females and 3 males.
00:16
So first question is number of different 6 member committees are possible if there are no restrictions.
00:42
Hence the number of ways equal to 9c6 which is equal to 9 factorial.
00:49
By 6 factorial multiplied by 3 factorial which is 9 multiplied by 8 multiplied by 7 multiplied by 6 factorial divided by 6 factorial multiplied by 3 factorial so we can cancel this and we have left out with 9 multiplied by 8 multiplied by 7 divided by 3 multiplied by 2 now we can cancel this 3 and 9 4 times sorry 3 times then 2 and 8 4 times then we will get 12 multiplied by 7 which is 54.
01:23
Therefore, this can be done in 54 ways.
01:30
Next one, the number of six -member committees are formed with exactly two gales.
01:39
So, number of different six -member committees are possible if there are exactly two girls.
02:04
So from this we can say so six member committee equal to it consists of two females plus four males.
02:23
Hence the number of ways equal to...