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    • Thread Starter

    I have the question: "If 6 people from a group of 5 men and 5 women are selected to pose for a photograph, if at least 2 of the selection must be men then how many different ways can the 6 people be chosen."
    In the answer given in the book they work out the number of ways with 2 men, then with 3 men, then 4 then 5. They then add them together to get the total different combinations with at least two men.
    I understand how this works but I cannot figure out why 5C2 x 8C4 doesn't also give the right answer. If you are multiplying the number of ways you can select two men by the number of ways you can select the four other 'photographee's' from the remaining 8 men or women, then I can't for the life of me figure out why this doesn't give all the ways you can form a group with two or more men.
    I am sure it's really obvious but I'd REALLY appreciate if someone can point out where I'm going wrong, thanks

    your way counts too many.
    if the men are a,b,c,d,e and women A,B,C,D,E then you will count picking a b as the 2 men


    but you will also count this variation, picking a and e as the 2 men

    • Thread Starter

    Thanks a lot It does seem obvios now
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