A class contains l0 students. Find the number n of ordered samples of size 4: With replacement; and Without replacement?
With replacement:
To find the number of ordered samples of size 4 with replacement, we can use the formula n^r, where n is the number of items (in this case, the number of students) and r is the size of the sample. So, for this problem:
n = 10 (the number of students)
r = 4 (the size of the sample)
n^r = 10^4 = 10,000
Therefore, there are 10,000 ordered samples of size 4 with replacement.
Without replacement:
To find the number of ordered samples of size 4 without replacement, we can use the formula nPr, which stands for the number of permutations of n items taken r at a time, without replacement. The formula is:
nPr = n! / (n-r)!
Where n! (n factorial) means n x (n-1) x (n-2) x ... x 2 x 1.
So, for this problem:
n = 10 (the number of students)
r = 4 (the size of the sample)
nPr = 10! / (10-4)! = 10 x 9 x 8 x 7 = 5,040
Therefore, there are 5,040 ordered samples of size 4 without replacement.