in how many ways, can we select a team of 4 students from a given choice of 15?
In how many ways can we select a team of 4 students from a given choice of 15?
Answer:
The problem of selecting a team of 4 students from a group of 15 can be solved using combinations, a fundamental concept in combinatorics. The formula to calculate the number of ways to choose ( k ) elements from a set of ( n ) distinct elements is given by the binomial coefficient formula ( C(n, k) = \frac{n!}{k!(n-k)!} ), where ( n! ) denotes the factorial of ( n ).
In this case, we are selecting a team of 4 students from 15. Thus, the number of ways to do this is given by
C(15, 4) = \frac{15!}{4!(15-4)!} .
Calculating this value gives us:
C(15, 4) = \frac{15!}{4!11!} = \frac{15 \times 14 \times 13 \times 12}{4 \times 3 \times 2 \times 1} = 1365 .
Therefore, there are 1365 ways to select a team of 4 students from a group of 15.