Question

In how many ways can a student answer 10 questions out of 13 questions in an exam if
the first two questions are compulsory? Also find the number of ways a student can
select the questions, if he must answer at least 3 out of the first 5 questions.​

Answer 1

Step-by-step explanation:

Questions to be answered in all =10 out of 13

Condition

Must choose at least 4 from first 5

Cases

(i) chooses 4 out of first 5

Number of ways to choose 4 from first 5=5C4=5

Chooses 6 from remaining 8

Number of ways to choose 6 from 8=8C6=28

Hence total number of ways to select 10 from 13=5×28=140

(ii) chooses 5 out

Answer 2

Answer:

questions to be answered =10 out of 13

Step-by-step explanation:

condition:

must choose at least 4 from first 5

cases:

chose 4 out of first 5

number of waysto choose 4 from 5=5c4=5

choose 6 from remaining 5

number of ways to choose 6 from 8=8c6=28

hence total number of ways to select 10 from13=5×28=140

choose 5 out

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