How many ways can 3 students be chosen from a class of 16 to represent their class at a banquet?
3,360
1,680
1,120
560
I think its 560.
(16*15*14)/3! = 560
you are correct
To determine the number of ways 3 students can be chosen from a class of 16 to represent their class at a banquet, we can use the combination formula. The combination formula is given by:
C(n, r) = n! / (r!(n-r)!)
Where n is the total number of students in the class (16 in this case) and r is the number of students to be chosen (3 in this case).
Using this formula, we can calculate the number of ways as follows:
C(16, 3) = 16! / (3!(16-3)!)
= 16! / (3! * 13!)
= (16 * 15 * 14) / (3 * 2 * 1)
= 560
Therefore, there are 560 ways to choose 3 students from a class of 16 to represent their class at a banquet. Your answer is correct.
To find the number of ways 3 students can be chosen from a class of 16, we can use the formula for combinations, which is given by:
C(n, r) = n! / (r!(n - r)!)
Where n is the total number of students in the class (16) and r is the number of students to be chosen (3).
Applying this formula:
C(16, 3) = 16! / (3!(16 - 3)!)
= (16 * 15 * 14 * 13!) / (3! * 13!)
= (16 * 15 * 14) / (3 * 2 * 1)
= 3360 / 6
= 560
So you are correct, there are 560 ways to choose 3 students from a class of 16 to represent their class at a banquet.