Permutations And Combinations

Question
CBSEENMA11014199

In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?

Solution

      Number of players = 17 (5 bowlers + 12 others)
Number of players to be selected = 11 (4 bowlers + 7 others)
Number of selections for 4 bowlers out of 5 = straight C presuperscript 5 subscript 4 space equals space fraction numerator 5 factorial over denominator 4 factorial space space 1 factorial end fraction equals 5              ...(i)
Number of selections for the remaining 7 players out of 12
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#6 {main}</pre>
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#6 {main}</pre>             ...(ii)
Hence, from (i) and (ii), by fundamental principle of counting, the number of ways in which the team can be selected = 5 x 792 = 3960

Some More Questions From Permutations and Combinations Chapter

Determine K, so that K + 2, 4K – 6 and 3K – 2 are three consecutive terms of an A.P.