The board of directors of a Student Center must be made up of 2 students from the 2nd year and 3 students from the 3rd. Knowing that 6 students from the 2nd year and 8 students from the 3rd year must be chosen for these positions, the number of ways to form the board of directors of the Student Center is: A) 71 B) 56 C) 840 D) 15

Question

The board of directors of a Student Center must be made up of 2 students from the 2nd year and 3 students from the 3rd. Knowing that 6 students from the 2nd year and 8 students from the 3rd year must be chosen for these positions, the number of ways to form the board of directors of the Student Center is: A) 71 B) 56 C) 840 D) 15

Answer 1

So you are choosing 2 from the 6 year2 students, and 3 from the 8 year3 students

number of ways = C(6,2)*C(8,3)
= 15*56
= 840

Carefully study and remember this type of question as a standard in the study of combinations.

Also noted that I ignored the poor wording in
"Knowing that 6 students from the 2nd year and 8 students from the 3rd year must be chosen for these positions"

We were NOT choosing 6 students from the 2nd year, we were choosing 2 of the 6 students from the 2nd year, etc