Home / Assignment Help / A test consists of 20 problems and students are told to answer any 15 of these questions. In how many different ways can they choose the 15 questions? a. 15,504 b. 20,145 c. 23,670 d. 25,890

A test consists of 20 problems and students are told to answer any 15 of these questions. In how many different ways can they choose the 15 questions? a. 15,504 b. 20,145 c. 23,670 d. 25,890

You need to determine the number of ways in which 30 competitors from 50 can qualify. First, you have to realize that the order is irrelevant, that is: it is the same competitor_1, competitor _2, competitor _3 than competitor_3, competitor_2, competitor_1, or any combination of those three competitors.

So, the number of ways is which 30 competitors from 50 can qualify is given by the formula of combinations, which is:

C (m,n) = m! / (n! * (m -n)! )

=> C (50,30) = 50! / (30! (50 – 30)! ) = (50!) / [30! (50 – 30)!] = 50! / [30! 20!] =

 = 47,129,212,243,960 different ways the qualifiying round of 30 competitors can be selected from the 50 competitors.

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