Question

In an examination paper on Business Mathematics,there are 14 questions divided into three groups of 5,5 and 4 questions respectively.A candidate is required to answer 6 questions taking at least two questions from each of the first groups and one question from the third group.In how many different ways can he make up his choice?​

Answer 1

Given : In an examination paper on Business Mathematics, there are 14 questions divided into three groups of 5,5 and 4 questions respectively.

A candidate is required to answer 6 questions taking at least two questions from each of the first two groups and one question from the third group.

To Find : In how many different ways can he make up his choice ​

Solution:

Minimum required

Group 1    = 2

Group  2 =  2

Group 3  =  1

Total = 6 hence 6th can be from any of one group

so there are 3 possible cases

( 3  , 2 ,  1  )  ,  ( 2  , 3   , 1 )  ,  ( 2 , 2 , 2)

So number of ways  =  ⁵C₃*⁵C₂*⁴C₁   +  ⁵C₂*⁵C₃*⁴C₁ +  ⁵C₂*⁵C₂*⁴C₂

=  10 * 10 * 4 +  10 * 10 * 4  + 10 * 10 * 6

=  400 + 400  + 600

= 1400

There are 1400 ways  he make up his choice

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Answer 2

Given : In an examination paper on Business Mathematics, there are 14 questions divided into three groups of 5,5 and 4 questions respectively.

A candidate is required to answer 6 questions taking at least two questions from each of the first two groups and one question from the third group.

To Find : In how many different ways can he make up his choice

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Minimum required

Group 1    = 2

Group  2 =  2

Group 3  =  1

Total = 6 hence 6th can be from any of one group

so there are 3 possible cases

( 3  , 2 ,  1  )  ,  ( 2  , 3   , 1 )  ,  ( 2 , 2 , 2)

So number of ways  =  ⁵C₃*⁵C₂*⁴C₁   +  ⁵C₂*⁵C₃*⁴C₁ +  ⁵C₂*⁵C₂*⁴C₂

=  10 * 10 * 4 +  10 * 10 * 4  + 10 * 10 * 6

=  400 + 400  + 600

= 1400

There are 1400 ways  he make up his choice

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