Question 40

Explanation

To solve this combination problem, first determine which questions are required and how many questions still need to be selected.

Identifying the Conditions

1. Total number of questions is $10$ questions
2. Questions to be worked on are $7$ questions
3. Required questions are numbers $1$, $2$, and $3$

Determining Questions to be Selected

Since participants must work on questions number $1$, $2$, and $3$, participants have already worked on $3$ questions.

Questions still to be selected

Determining Available Questions to Choose From

Available questions to choose from are those other than numbers $1$, $2$, and $3$

Number of available questions to choose from

Calculating the Number of Ways to Choose

Participants must choose $4$ questions from $7$ available questions. Use combination

Therefore, the number of ways participants can choose the questions to work on is $35$ ways.