How many subsets of {2, 3, 4, 5, 6, 7, 8, 9} contain at least one prim

Question

How many subsets of {2, 3, 4, 5, 6, 7, 8, 9} contain at least one prime number?

(A) 128
(B) 192
(C) 224
(D) 240
(E) 256}

Lampard42 · Accepted Answer

Total number of subsets = 2^8 = 256
Total number of non prime numbers = 4,6,8,9 = 4. Number of possible subsets with only these numbers = 4c1+4c2+4c3+4c4 + 1(for null set) = 4+6+4+1+1= 16.

So non prime subsets = 256-16 = 240 Option D

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LeoN88 · Answer

Arvind's method is better: All- (Only Composite number sub sets); just make sure you include the null set.

The long cut method-

Non prime= 2,4, 6 and 8.

Subsets containing-
1. Exactly one prime= 4 * (4C0 + 4C1 + 4C2 + 4C3 + 4C4)
2. Exactly two primes= 4C2 * (4C0 + 4C1 + 4C2 + 4C3 + 4C4)
3. Exactly three primes= 4C3 * (4C0 + 4C1 + 4C2 + 4C3 + 4C4)
4. Exactly four primes=1 * (4C0 + 4C1 + 4C2 + 4C3 + 4C4)

Answer= 2^4 * (4+6+4+1)= 15*16= 240

ChiragSabharwal · Answer

Total no. of subsets from {2, 3, 4, 5, 6, 7, 8, 9} = 2^8 = 256 --->> A
Total no. of subsets that do not contain any prime from {4, 6, 8, 9} = 2^4 = 16 --->> B
Total no. of subsets that contain at least one prime = A - B = 240

Fdambro294 · Answer

For each number, we can decide whether the Number is “IN” a given set or “OUT” of the given set.

Total Number of Sets Possible:

2 ——- in or out——— 2 options
And
3 ——- in or out ———- 2 options 
And
4——- in or out ———- 2 options

.....
9 —— in or out ——— 2 options
_____________________

This gives us (2)^8 possibilities (which includes all the subsets that have one or two or three or four ....up to all eight of the numbers)

However, this also includes the 1 “empty subset” in which no numbers are included in the subset. So we need to subtract this one possibility out.

Total possible sets = (2)^8 - 1 = 255

From the total possible subsets, we need to Remove all of the cases that do NOT include at least 1 Prime number. These will be:

2——out

3——out

4 ——-IN or OUT —— 2 options

5——-out

6—— IN or OUT ——- 2 options

7——out

8—— IN or OUT ——2 options

9—— IN or OUT ——- 2 options
________________

(2)^4 subsets

However, again we need to remove the 1 possibility of the “empty subset” in which no numbers are included (they are all “out”)

(2)^4 - (1) = 15

255 - 15 = 240 subsets that include at least 1 prime number

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anish777 · Answer

should not the answer be 239 ? As in one case we are considering all the 4 prime and all the 4 non-prime numbers, which is not a subset of the set mentioned.

Bunuel · Answer

No, becaseu a set is a subset of itself. Hence, {2, 3, 4, 5, 6, 7, 8, 9} is a subset of {2, 3, 4, 5, 6, 7, 8, 9}.

OmerKor · Answer

Hi  Bunuel ,

Although I practiced 95% of the topics in Quant I found that I have a little gap in this topic.
Do you have an explanatory post on this topic? of the concept "Subsets" - computing / formulas / general idea behind it?

Thanks!

bumpbot · Answer

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How many subsets of {2, 3, 4, 5, 6, 7, 8, 9} contain at least one prim

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How many subsets of {2, 3, 4, 5, 6, 7, 8, 9} contain at least one prim

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