students are given a list of 10 vocbulary words to learn. in how many ways could four of the wwords be listed on the test? if wrong give correct answers please my answer is 3780.
To find the number of ways to choose four vocabulary words from a list of ten, we can use the concept of combinations. Specifically, we want to find the value of "10 choose 4" denoted as C(10, 4) or 10C4.
The formula for combinations is given by:
C(n, r) = n! / (r!(n-r)!),
where "n" represents the total number of items and "r" represents the number of items to be selected.
In our case, we have n = 10 (total number of vocabulary words) and r = 4 (number of words to be selected).
Now, let's calculate using the formula:
C(10, 4) = 10! / (4! * (10-4)!)
= 10! / (4! * 6!)
= (10 * 9 * 8 * 7 * 6!) / (4! * 6!)
= (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)
= 5040 / 24
= 210.
Therefore, there are 210 ways to list four vocabulary words on the test, not 3780 as mentioned in your answer.