How many ways can 3 students be chosen from a class of 16 to represent their class at a banquet?
A. 3,360
B. 1,680
C. 1,120
D. 560
What is
C(16,3) ?
Reiny, 16 times 3 is 48. You are wrong.
To find the number of ways to choose 3 students from a class of 16, we can use the combination formula: nCr = n! / ((n-r)! * r!), where n is the total number of students in the class and r is the number of students we want to choose.
In this case, n = 16 and r = 3:
16C3 = 16! / ((16-3)! * 3!)
Calculating this:
16C3 = 16! / (13! * 3!)
= (16 * 15 * 14 * 13!) / (13! * 3 * 2 * 1)
= (16 * 15 * 14) / (3 * 2 * 1)
= 5,040 / 6
= 840
Therefore, the number of ways to choose 3 students from a class of 16 is 840.
The correct answer is not listed among the options provided.
To find the number of ways to choose 3 students from a class of 16, we can use the concept of combinations. The formula for combinations is given by:
C(n, r) = n!/((n-r)! * r!)
where n is the total number of items, and r is the number of items to be chosen.
In this case, n = 16 (total number of students) and r = 3 (number of students to be chosen). Plugging in these values into the formula, we get:
C(16, 3) = 16!/((16-3)! * 3!)
Calculating the values:
16! = 16 * 15 * 14 * 13 * ... * 1
(16-3)! = 13! = 13 * 12 * 11 * ... * 1
3! = 3 * 2 * 1
Simplifying further, we get:
C(16, 3) = (16 * 15 * 14 * 13!) / (13! * 3 * 2 * 1)
The 13! cancels out from the numerator and denominator:
C(16, 3) = (16 * 15 * 14) / (3 * 2 * 1)
Calculating the values:
C(16, 3) = (16 * 15 * 14) / (6)
C(16, 3) = (3360) / (6)
C(16, 3) = 560
Therefore, the correct answer is option D. 560.