Question

In a group of students, there are 3 boys and 4 girls. Four students are to be selected at random from the group. Find the probability that either 3 boys and 1 girl or 3 girls and 1 boy are selected.

Answer 1

Answer:

16/35

Step-by-step explanation:

Hi,

Given a group of students in which there are 3 boys and 4

girls,in which 4 students are selected randomly. Since there are

in total 7 children(3 boys + 4 girl) the possible number of ways of

choosing 4 students out of 7 are ⁷C₄

Number of ways of selecting 3 boys and 1 girl would be

³C₃*⁴C₁ = 4

Number of ways of selecting 1 boy and 3 girls would be

³C₁*⁴C₃ = 12

Total number of ways of selecting either 3 boys and 1 girl

or 3 girls and 1 boy are (4 + 12) = 16

Probability that either 3 boys and 1 girl or 1 boy and 3 girls will be

selected = Total number of ways of selecting either 3 boys and 1

girl or 3 girls and 1 boy/ Total number of ways of selecting 4

children

= 16/35

Hope, it helps !