Question
From 10 musicians and 5 singers, a band of 8 members is to
be formed. In how many ways can the band be formed such that there are at least 6 musicians?Solution
Case I: 6 musicians and 2 singers
Number of ways = 10C6 × 5C2 = 210 × 10 = 2100 ways
Case II: 7 musicians and 1 singer
Number of ways = 10C7 × 5C1 = 120 × 5 = 600 ways
Case III: 8 musicians and 0 singers
Number of ways = 10C8 × 5C0 = 45 × 1 = 45 ways
Total number of ways = 2100 + 600 + 45 = 2745 ways
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