Suppose that an exam has 29 questions on it and students need to answer 20 of th

Question

Suppose that an exam has 29 questions on it and students need to answer 20 of the questions. In how many ways can this be done if the first 4 questions and exactly 5 of the last 7 questions must be answered? Skat is a card game that uses a 32-card deck (which can be formed by removing all of the 2's, 3's, 4's, 5's, and 6's from a standard 52-card deck) in which the players are each dealt a hand from the deck of 32. Suppose that you are playing Skat and are dealt an 8-card hand. What is the probability that you are dealt no more than 1 jack? What is the probability that you are dealt exactly 3 diamonds and no sevens?

Explanation / Answer

6) there are a total of 29 questions and 20 questions must be answered , this can be done in 29C20 ways

now first 4 can be answered in 4C4 ways and 5 out of last 7 can be answered in 7C5 ways , now 9 questions are taken care of , so we are left with 20-9 = 11 questions to answer out of 29-7-4 = 18 questions , so the remaining questions can be answered in 18C11 ways

so finally the question can be answered as

4C4 *7C5 * 18C11 =

using the combination formula of nCr = n!/r!(n-r)!

1*21*31824 = 668304 ways

Please note that we can answer only 1 question at a time , as per the answering guidelines

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