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  • A family has 4 members, 5 friends and 2 guests. The family car can accommodate only 4 persons. In no way the guests cannot be refused to avail the car in any trip. In how many ways can th

A family has 4 members, 5 friends and 2 guests. The family car can accommodate only 4 persons. In no way the guests cannot be refused to avail the car in any trip. In how many ways can the car accommodate?

Option: 1

46


Option: 2

42


Option: 3

60


Option: 4

36


Answers (1)

best_answer

Note the following:

  • The formula for the combination for the selection of the \mathrm{x} items from the \mathrm{y}different items is \mathrm{=^{y}C_{x}=\frac{y!}{x!\left ( y-x \right )!}}

  • The restricted combination for the selection of the \mathrm{r} items from the \mathrm{n}different items with \mathrm{k} particular things always included is \mathrm{=^{n-k}C_{r-k}}

Since 2 guests must always be accommodated in the family car, the following is evident.

  • The number from which the restricted combination is to be made is \mathrm{=n-k=(4+5+2)-2=11-2=9}.

  • The number with which the restricted combination is to be made is \mathrm{=r-k=4-2=2}

Therefore, the required restricted combination is

=\mathrm{^{n-k}C_{r-k}}

=\mathrm{^{9}C_{2}}

=\frac{9!}{2!7!}

=36

Posted by

vinayak

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