A father with 8 children takes them 3 at a time to the zoological garden, as often as he can without taking the same 3 children together more than once. The number of times he will go to the garden is

Question

A father with 8 children takes them 3 at a time to the zoological garden, as often as he can without taking the same 3 children together more than once. The number of times he will go to the garden is (A) 56 (B) 100 (C) 112 (D) None of these

Tardigrade Admin · Accepted Answer

Number of times he will go to garden = Number of ways of selecting 3 children from 8 children = 8 C 3=(8 × 7 × 6/3 × 2)=56

Q. A father with $8$ children takes them $3$ at a time to the zoological garden, as often as he can without taking the same $3$ children together more than once. The number of times he will go to the garden is

56

100

112

None of these

Number of times he will go to garden
$=$ Number of ways of selecting 3 children from
$8$ children $=^{8} C_{3} = \frac{8 \times 7 \times 6}{3 \times 2} = 56$

Q. A father with 8 children takes them 3 at a time to the zoological garden, as often as he can without taking the same 3 children together more than once. The number of times he will go to the garden is

56

100

112

None of these

Number of times he will go to garden = Number of ways of selecting 3 children from 8 children =8C3​=3×28×7×6​=56

Q. A father with $8$ children takes them $3$ at a time to the zoological garden, as often as he can without taking the same $3$ children together more than once. The number of times he will go to the garden is

Number of times he will go to garden
$=$ Number of ways of selecting 3 children from
$8$ children $=^{8} C_{3} = \frac{8 \times 7 \times 6}{3 \times 2} = 56$