How many 3 element subsets are there in the set {a,b,c,d,e,f,g}a.7b.140c.70d.21e.35
Question
How many 3 element subsets are there in the set {a,b,c,d,e,f,g}a.7b.140c.70d.21e.35
Solution
The number of 3-element subsets in a set can be calculated using the combination formula, which is nCr = n! / [(n-r)! * r!], where n is the total number of elements in the set, r is the number of elements in each subset, and "!" denotes factorial.
In this case, the set {a,b,c,d,e,f,g} has 7 elements (n=7), and we want to find the number of 3-element subsets (r=3).
So, we plug these values into the combination formula:
7C3 = 7! / [(7-3)! * 3!] = 7! / [4! * 3!] = (765) / (321) = 35
So, there are 35 3-element subsets in the set {a,b,c,d,e,f,g}. Therefore, the correct answer is e.35.
Similar Questions
3. How many subsets of {a, b, c, d, e, f, h, i} are there? Show how you determined it.
If A = {a, b, c} then the number of possible subsets isA.3B.8C.6D.None of these
How many functions are there form the set {A, B, C, D} to the set {1, 2, 3}?Select one:a.43b.0c.None of the othersd.34e.12
How many subsets of the set {1, 2, 3, 4} that contain 3?Select one:a.9b.3c.8d.16
3. If set A has 3 elements then number of elements in A X A X A are __________a) 9b) 27c) 6d) 19
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.