Most Important Selected Qs for JEE AdvancedMathematicsPermutation and Combination
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:
Options
- Athere are exactly 3 indian classic songs in top 5 is (5 !)^3
- Btop rank goes to indian classic song is 6.9 !
- Cthe ranks of all western songs are consecutive is 4 ! 7 !
- Dthe 6 indian classic songs are in a specified order is ¹⁰ P₄
Correct answer
D. the 6 indian classic songs are in a specified order is ¹⁰ P₄
Step-by-step solution
(a) Number of ways = ^6 C₃ ^4 C₂ 5 ! 5 !=(5 !)^3 (b) Number of ways = ^6 C₁ 9 !=6 9 ! (c) Number of ways =(6+1) ! 4 !=7 ! 4 ! (d) Number of ways = ¹⁰ C₆ 1 4 != ¹⁰ C₄ 4 != ¹⁰ P₄