If set A={a,b,c,d,e}, what is the number of subsets that must include

Question

If set A={a,b,c,d,e}, what is the number of subsets that must include only 3 elements?

A. 8 
B. 10 
C. 12 
D. 15 
E. 18

sashiim20 · Accepted Answer

Set A={a,b,c,d,e}

Number of ways to select 3 elements from set of 5 elements \(= \frac{5!}{3!(5-3)!}\)

\(\frac{5!}{3!2!} = \frac{5 * 4* 3*2}{3*2 * 2} = 5 * 2 = 10\). Answer (B)...

Leo8 · Answer

Chosing 3 elements out of 5 : 5c3 = 10 = B

danlew · Answer

Question asks how many ways can you choose 3 items out of 5 = 5C3 = 10
Answer B

MathRevolution · Answer

==> You get 5C3=5C2=(5)(4)/2!=10.

The answer is b.
Answer: B

ydmuley · Answer

If set A={a,b,c,d,e}, what is the number of subsets that must include only 3 elements?

= 5C2

= \frac{5!}{2! * 3!}

= 5 * 2

= 10

Hence, Answer is B

Umber · Answer

10 is the wrong answer here; it must be option  D.15 .

3 element subset of A{a,b,c,d,e} = 5C3 + 5.

5 needs to be added up to consider  {a,a,a} ; {b,b,b} ; {c,c,c} ; {d,d,d} ; {e,e,e}  which are also the subsets of A.

Sometimes, little problems can be tricky! Kuddos if you agree!

onlymalapink · Answer

doesnt the combination formula count this by default?

Umber · Answer

Nope 5C3 will be: 10

abc ; abd ; abe ; acd ; ace ; ade ; bcd ; bce ; bde ; cde

If set A={a,b,c,d,e}, what is the number of subsets that must include

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GMAT Problem Solving (PS) Questions

If set A={a,b,c,d,e}, what is the number of subsets that must include

Prep Toolkit

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More than Quant/Verbal Abilities: Speed vs. Accuracy

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My Rewards