Data management

from a group of 6 men and 7 women going on a trip, find the number of
a) ways of selecting a female tour guide, a female cook and a driver of either sex
b) ways of selecting a commitee of 5 people with 4 or more men

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  1. 7 ways for tour guide, then 6 ways for cook then 11 ways for driver
    7 * 6 * 11

    combinations of 5 out of the six men at a time
    6!/[ 5!(1!)] = 6
    combinations of 4 out of the 6 men
    6!/[ 4!(2!)] = 6*5/2 = 15
    If we have 4 men, then one of the 7 women must serve (we have already included the remaining two men in the five men option)
    so for each combination of 4 men we have a choice of 7 women
    so in all
    6 + 15 * 7

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  2. since there is a title for a job so

    (7 choose 2)(11 choose 1)

    11 because u already choose 2 women

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