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Q.

A contest consisting of ranking 10 songs of which 6 are Indian classic and 4 are western
songs. Number of ways of ranking so that:

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a

top rank goes to Indian classic song is 6.9!

b

the 6 Indian classic songs are in a specified order is $^{10} P_{4}$

c

the ranks of all western songs are consecutive is 4! 7!

d

there are exactly 3 Indian classic songs in top 5 is ${(5!)}^{3}$

answer is A, B, C, D.

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Detailed Solution

A) Number of ways $=^{6} C_{3} \times^{4} C_{2} \times 5! \times 5! = {(5!)}^{3}$
B) Number of ways $=^{6} C_{1} \times 9! = 6 \times 9!$
C) Number of ways $= (6 + 1)! \times 4! = 7! 4!$
D) Number of ways $=^{10} C_{6} \times 1 \times 4! =^{10} C_{4} \times 4! =^{10} P_{4}$

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