# In a certain examination you are required to answer six out of nine questions. find the number of ways that you can choose the six questions, (c)If at least four should be selected from the first...

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If at least four questions should be selected from the first five, that means you can select four questions and five questions from the first five questions. Find the combinations for each case separately, then add them all together.

4 questions (out of first five) 5 questions (out of first five)

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5 questions are to choose from 5 questions are to choose from

and you require 4: 5C4 ways and you require 5: 5C5 ways

Rest: 4 questions are to Rest: 4 questions are to

choose from and you choose from and you

require 2: 4C2 ways require 1: 4C1 ways

Total combinations: 5C4*4C2 Total combinations: 5C5*4C1

=5C1*4C2 =5*6= 30 =1*4 =4

Total number of ways = 30+4 = 34.

Therefore, the number of ways that you can choose the six questions, if at least four should be selected from the first five questions, is 34.