Out of 11 members of a family 4 are males and rest females. The family hired three taxis on rent to see a museum. The members have to sit in the cars in such a way that not more than 4 members are in any one car and each car has at least one male member. In how many different ways the members can travel?

Explanation:

Total members in the family = 11

Number of males = 4

Number of females = 7

Number of cars hired = 3

No car can have more than 4 members. So the possible combinations can be such that one car has 3 members and the other two cars 4 each.

Further, each car must have at least one male. The total no. of males is 4. So, only one car will have 2 males and the rest one each.

Option : I II III

Total members Possible : 3 4 4

combination : 1 m 1m 2m

and 1f and 3f and 2f

or or or

(2m 2m 1m

and 1f and 2f and 3f) x 2

Total number of ways

= (4C1×7C2+4C1×7C3+4C2×7C2+4C2×7C1+4C2×7C2+4C1×7C2)×2

= [4×21 + 4×35 + 6×21 + 6×7 + 6×21 + 4×35]×2

= 126 + 266 + 266

Total No. of ways = 126 + 266 + 266 = 658