The number of ways of selecting 15 teams from 15 men and 15 women,

such that each team consists of a man and a woman, is :

  • Option 1)

    1120

  • Option 2)

    1240

  • Option 3)

    1880

  • Option 4)

    1960

 

Answers (1)

As we learnt in

Theorem of Combination -

Each of the different groups or selection which can be made by taking r things from n things is called a combination.

^{n}c_{r}=\frac{(n)!}{r!(n-r)!}

- wherein

Where 1\leq r\leq n

 

 We use selections.

Total select one man and women out of 15 men and 15 women is ^{15}C_{1}\times^{15}C_{1}=225

For second team, we get ^{14}C_{1}\times^{14}C_{1}=196

and so on, we have 1^{2}+2^{2}+........+15^{2}=\frac{15\times16\times3}{6}=1240

Correct option is 2.

 


Option 1)

1120

This is an incorrect option.

Option 2)

1240

This is the correct option.

Option 3)

1880

This is an incorrect option.

Option 4)

1960

This is an incorrect option.

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