Consider the set A = {1, 2, 3, ....., 30}. The number of ways in which

1.	Consider the set A = {1, 2, 3, ....., 30}. The number of ways in which one can choose three distinct number from A so that the product of the chosen numbers is divisible by 9 is(a) 1590(b) 1505(c) 1110(d) 1025
Answer» Answer is : (a) 1590 Given, A = {1, 2, 3, …, 30} Case I All three number are multiple of 3 then product of three number are divisible by 9. ∴ ¹⁰C₃ = 120 Case II Two number are multiple of 3 and other are not multiple of 9. i.e. ¹⁰C₂ x²⁰C₁ = 900 Case III One are multiple of 9 and other two are not multiple of 3. ³C₁ x ²⁰C₂ = 570 ∴Total number of ways = 120+900+570 = 1590

Consider the set A = {1, 2, 3, ....., 30}. The number of ways in which one can choose three distinct number from A so that the product of the chosen numbers is divisible by 9 is(a) 1590(b) 1505(c) 1110(d) 1025

Answer»

Answer is : (a) 1590

Given, A = {1, 2, 3, …, 30}

Case I All three number are multiple of 3 then product of three number are divisible by 9.

∴ ¹⁰C₃ = 120

Case II Two number are multiple of 3 and other are not multiple of 9.

i.e. ¹⁰C₂ x²⁰C₁ = 900

Case III One are multiple of 9 and other two are not multiple of 3.

³C₁ x ²⁰C₂ = 570

∴Total number of ways = 120+900+570 = 1590

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Consider the set A = {1, 2, 3, ....., 30}. The number of ways in which one can choose three distinct number from A so that the product of the chosen numbers is divisible by 9 is(a) 1590(b) 1505(c) 1110(d) 1025

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