6 A new village social club has 10 members of whom 6 are men and 4 are women. The club committee will consist of 5 members.
- In how many ways can the committee of 5 members be chosen if it must include at least 2 men and at least 1 woman?
The 10 members of the club stand in a line for a photograph. - How many different arrangements are there of the 10 members if all the men stand together and all the women stand together?
For a second photograph, the members stand in two rows, with 6 on the back row and 4 on the front row. Olly and his sister Petra are two of the members of the club. - How many different arrangements are there of the 10 members in which Olly and Petra stand next to each other on the front row?
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