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A trust has 25 members. How many ways 3 officers can be selected?

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#### Solution

Number of members in the trust = 25

The number of ways of selecting 3 officers from 25 members is

= ^{25}C_{3}

= `(25!)/(3! xx (25 - 3)!)`

= `(25!)/(3! xx 22!)`

= `(25 xx 24 xx 23 xx 22!)/(3! xx 22!)`

= `(25 xx 24 xx 23)/(3 xx 2 xx 1)`

= 25 × 4 × 23

= 2300

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