In a department of biology, there are five professors and five students. if seven members of the department are randomly selected to form a committee for admission, and if the number of professors must be one more than students, how many combinations are possible?

There are 50 ways to select in this way and there is only 1 combination is possible i.e. 3 students and 4 professors.

Step-by-step explanation:

Since we have given that

Number of professors = 5

Number of students = 5

We need to find the number of ways of 7 members in such that number of professors must be one more than students.

So, if we select 3 students, then there will be 4 professors.

So, Number of ways would be

Hence, there are 50 ways to select in this way and there is only 1 combination is possible i.e. 3 students and 4 professors.