Problem:
A committee of 4 is to be formed among 4 girls and 5 boys. The probability that the committee will have the number of boys less than the number of girls is _______ . (Round off to three decimal places) Correct answer is between '0.165,0.168'.

Solution:
To find the probability that the committee will have the number of boys less than the number of girls, we need to calculate the favorable outcomes and divide it by the total number of possible outcomes.

Favorable Outcomes:
In order to have the number of boys less than the number of girls, there are three possible cases:

1. 1 boy and 3 girls:
- Number of ways to select 1 boy out of 5 boys: C(5, 1) = 5
- Number of ways to select 3 girls out of 4 girls: C(4, 3) = 4
- Total number of favorable outcomes for this case: 5 * 4 = 20

2. 2 boys and 2 girls:
- Number of ways to select 2 boys out of 5 boys: C(5, 2) = 10
- Number of ways to select 2 girls out of 4 girls: C(4, 2) = 6
- Total number of favorable outcomes for this case: 10 * 6 = 60

3. 3 boys and 1 girl:
- Number of ways to select 3 boys out of 5 boys: C(5, 3) = 10
- Number of ways to select 1 girl out of 4 girls: C(4, 1) = 4
- Total number of favorable outcomes for this case: 10 * 4 = 40

Total Outcomes:
The total number of ways to select a committee of 4 from 9 people (4 girls and 5 boys) is given by C(9, 4) = 126.

Probability:
The probability that the committee will have the number of boys less than the number of girls is the ratio of the favorable outcomes to the total outcomes.

Probability = (Total number of favorable outcomes) / (Total number of possible outcomes) = (20 + 60 + 40) / 126

Probability = 120 / 126

Probability ≈ 0.952

Rounding off to three decimal places, the probability is approximately 0.952.

Answer:
The probability that the committee will have the number of boys less than the number of girls is approximately 0.952.