A DJ has 20 songs to choose from and can only play 7 in the next half hour. 1)Ho

Question

A DJ has 20 songs to choose from and can only play 7 in the next half hour. 1)How many different combinations are possible if the Dj doesn't want to repeat songs? 2) A friend of the DJ dislikes 5 of the 20 songs. If the dj selects the 7 songs randomly, what is the probability that his friend will dislike at least one song played during the next half hour?
A DJ has 20 songs to choose from and can only play 7 in the next half hour. 1)How many different combinations are possible if the Dj doesn't want to repeat songs? 2) A friend of the DJ dislikes 5 of the 20 songs. If the dj selects the 7 songs randomly, what is the probability that his friend will dislike at least one song played during the next half hour?

Explanation / Answer

1. The answer to that is 20 pick 7, which is expressed as: 20! ------ 7!*13! This found on a TI 89 calculator by typing catalog, 6, enter.(This will give you the nCR function). Then you enter 20,7) it should look like this: nCR(20,7) The answer: 77520 2. Find the probability that the friend dislike none of the songs then take 1 minus that to find the probability that he will dislike 1 or more songs. The probability of picking 0 bad songs and 7 good songs out of the possible ways to pick 7 songs. This is equal to: 5! 15! --------- * --------- 5! * 0! 7! * 8! ------------------------- 20! ---------- 13! * 7! In a TI-89 calculator this would be: nCR(5,0)* nCR(15,7)/nCR(10,7) = 429/5168 Now take the complement (1- that probability): 1 - 429/5168 = 4739/5168 Answer: 4739/5168 or .917

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