In a group of artists, there are 10 dancers and 8 singers. If four artists are to be selected at random, what is the probability that 2 dancers and 2 singers are selected?

Total number of artists = 10 + 8 = 18 Let S be the sample space. Then, n(S) = number of ways selecting 4 artists out of 18 = ^{18}C_{4} = (18 × 17 × 16 × 15)/(3 × 2 × 1) = 3060 Let E= event of selecting 2 dancers and 2 singers n(E) = ¹°C_2×⁸C_2 = (10 × 9 )/(2 ×1) x (8 × 7)/(2 ×1) = 45× 28 = 1260 ∴ P (E) = n(E)/n(S) = 1260/3060 = 7/17

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