Find the number of different ways that an instructor can choose 7 students from a class of 35 students for a field trip.
To find the number of different ways an instructor can choose 7 students from a class of 35 students, we can use the combination formula.
The combination formula is given by C(n, r) = n! / (r! * (n - r)!)
In this case, we want to choose 7 students from a class of 35, so n = 35 and r = 7. Plugging these values into the formula, we get:
C(35, 7) = 35! / (7! * (35 - 7)!)
We can simplify the formula by canceling out the factorials:
C(35, 7) = 35 * 34 * 33 * 32 * 31 * 30 * 29 / (7 * 6 * 5 * 4 * 3 * 2 * 1)
Computing the numerator and denominator separately:
Numerator: 35 * 34 * 33 * 32 * 31 * 30 * 29 = 2,908,176,320
Denominator: 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5,040
Dividing the numerator by the denominator:
C(35, 7) = 2,908,176,320 / 5,040 = 581,959
Therefore, there are 581,959 different ways the instructor can choose 7 students from the class.