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2 October, 00:34

Twenty-one boys and eight girls go on a camping trip. In how many ways can a group of six be selected to gather firewood, given the following conditions?

(a) The group consists of two girls and four boys.

(b) The group contains at least two girls.

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  1. 2 October, 01:06
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    (a) there are 8C2 = 28 ways of picking 2 girls from 8

    And there are 21C4 = 5985 ways of picking 4 boys

    Required number of ways for 2g / 4b = 28 * 5985 = 167,580

    (b) at least 2 girls means combinations of 2g/4b, 3g, 3b, 4g/2b, 5g 1b or

    6 girls.

    2g/4b = 167,580 ways

    3g/3b = 8C3 * 21C3 = 56 * 1330 = 74,480

    4g/2b = 8C4 * 21C2 = 70 * 210 = 14,700

    5g 1b = 8C5 * 21 = 56*21 = 1176

    6 girls = 8C6 = 28

    adding these up we get the answer to (b) which is 257,964
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