Question

Let S = {1, 2, 3, 4, 5, 6} a. How many subsets are there of cardinality 4? (Note: you can enter "C(n,k)" for (n k).) b. How many subsets of cardinality 4 have {2, 3, 5} as a subset? c. How many subsets of cardinality 4 contain at least one odd number? d. How many subsets of cardinality 4 contain exactly one even number?

          Let S = {1, 2, 3, 4, 5, 6}
a. How many subsets are there of cardinality 4?
(Note: you can enter "C(n,k)" for (n
k).)
b. How many subsets of cardinality 4 have {2, 3, 5} as a subset?
c. How many subsets of cardinality 4 contain at least one odd number?
d. How many subsets of cardinality 4 contain exactly one even number?

Let S = 1, 2, 3, 4, 5, 6
a. How many subsets are there of cardinality 4?
(Note: you can enter "C(n,k)" for (n
k).)
b. How many subsets of cardinality 4 have 2, 3, 5 as a subset?
c. How many subsets of cardinality 4 contain at least one odd number?
d. How many subsets of cardinality 4 contain exactly one even number?

Added by Charles K.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Supreeta N

04/04/2023

Step 1

In this case, n = 6 and k = 4. C(6, 4) = 6! / (4!(6-4)!) = 6! / (4!2!) = (6*5*4*3*2*1) / ((4*3*2*1)*(2*1)) = (6*5) / (2*1) = 15 So there are 15 subsets of cardinality 4. b. Show more…

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Let S = {1, 2, 3, 4, 5, 6} a. How many subsets are there of cardinality 4? (Note: you can enter "C(n,k)" for (n k).) b. How many subsets of cardinality 4 have {2, 3, 5} as a subset? c. How many subsets of cardinality 4 contain at least one odd number? d. How many subsets of cardinality 4 contain exactly one even number?