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A sports fan is deciding which of 6 baseball cards to be purchase. Two

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A sports fan is deciding which of 6 baseball cards to be purchase. Two  [#permalink]

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New post 01 Mar 2019, 11:20
1
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A
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Difficulty:

  25% (medium)

Question Stats:

72% (01:40) correct 28% (01:49) wrong based on 32 sessions

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A sports fan is deciding which of 6 baseball cards to be purchase. Two cards feature pitchers, two cards feature catchers and two feature outfielders. If the sports man plans to purchase 3 cards and decides that one card (and only one card) must be a pitcher, then how many combinations of baseball cards could he purchase (assume that the order of cards does not matter)?
(A) 9
(B) 12
(C) 18
(D) 20
(E) 30

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A sports fan is deciding which of 6 baseball cards to be purchase. Two  [#permalink]

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New post Updated on: 01 Mar 2019, 14:40
topper97 wrote:
A sports fan is deciding which of 6 baseball cards to be purchase. Two cards feature pitchers, two cards feature catchers and two feature outfielders. If the sports man plans to purchase 3 cards and decides that one card (and only one card) must be a pitcher, then how many combinations of baseball cards could he purchase (assume that the order of cards does not matter)?
(A) 9
(B) 12
(C) 18
(D) 20
(E) 30


Hi,
Since 1 of the three must be a pitcher, left to choose 2 from 4. 4C2 = 6.
now, possible combinations = (two pitcher cards)2 * 6 = 12

Option B

Thanks.
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Originally posted by Doer01 on 01 Mar 2019, 14:28.
Last edited by Doer01 on 01 Mar 2019, 14:40, edited 1 time in total.
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Re: A sports fan is deciding which of 6 baseball cards to be purchase. Two  [#permalink]

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New post 01 Mar 2019, 14:34
There are two pitcher cards we can choose, so we just need to look at the Combination for how to choose the other 2 cards. With the other 2 cards, we have 4 options (two catchers and two outfielders). Honestly, these numbers are so small, you could just count the options.

ABCD ---> AB, AC, AD, BC, BD, CD
There are six ways to choose the other 3 cards.

Those 6 ways x 2 possible pitches = 12.
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Re: A sports fan is deciding which of 6 baseball cards to be purchase. Two   [#permalink] 01 Mar 2019, 14:34
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