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21 Mar 2023, 01:30
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D
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Difficulty:
35%
(medium)
Question Stats:
75% (02:09) correct
25%
(02:41)
wrong
based on 57
sessions
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For his birthday, Brian will receive either three or four differently colored ties, either two or three differently colored shirts, and either one or two differently colored jackets. Depending on how many ties, shirts, and jackets he receives, which of the following values could be the number of ways he could make an outfit with one tie, one shirt, and one jacket?
I. 10
II. 16
III. 18
A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III
I. 10
II. 16
III. 18
A. I only
B. II only
C. I and II only
D. II and III only
E. I, II, and III
21 Mar 2023, 02:11
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Brian will receive
Ties - 3/4
Shirts - 2/3
Jacket - 1/2
Depending on how many ties, shirts, and jackets he receives, which of the following values could be the number of ways he could make an outfit with one tie, one shirt, and one jacket?
the possible combinations are - 6, 8, 12, 16, 18, 24
So, only 16 and 18 are given in II and III option.
Answer D
Ties - 3/4
Shirts - 2/3
Jacket - 1/2
Depending on how many ties, shirts, and jackets he receives, which of the following values could be the number of ways he could make an outfit with one tie, one shirt, and one jacket?
the possible combinations are - 6, 8, 12, 16, 18, 24
So, only 16 and 18 are given in II and III option.
Answer D
22 Mar 2023, 20:04
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=To pick his outfit, Brian should choose between 3 or 4 different ties, 2 or 3 different shirts, and 1 or 2 different jackets.
This can be done if he receives;
3 shirts, 2 ties, 1 jacket(s) or
3 shirts, 3 ties, 1 jacket(s) or
3 shirts, 2 ties, 2 jacket(s) or
3 shirts, 3 ties, 2 jacket(s) or
4 shirts, 2 ties, 1 jacket(s) or
4 shirts, 3 ties, 1 jacket(s) or
4 shirts, 2 ties, 2 jacket(s) or
4 shirts, 3 ties, 2 jacket
We have to find out combinations for each set(have to pick 1 from each shirt, tie and jacket) and match from questions-
So 3 shirts, 2 ties, 1 jacket(s) = 3C1 * 2C1 * 1C1 = 6 ways
3 shirts, 3 ties, 1 jacket(s) = 3C1 * 3C1 * 1C1 = 9 ways
3 shirts, 2 ties, 2 jacket(s) = 3C1 * 2C1 * 2C1 = 12 ways
3 shirts, 3 ties, 2 jacket(s) = 3C1 * 3C1 * 2C1 = 18 ways
4 shirts, 2 ties, 1 jacket(s) = 4C1 * 2C1 * 1C1 = 8 ways
4 shirts, 3 ties, 1 jacket(s) = 4C1 * 3C1 * 1C1 = 12 ways
4 shirts, 2 ties, 2 jacket(s) = 4C1 * 2C1 * 2C1 = 16 ways
4 shirts, 3 ties, 2 jacket(s) = 4C1 * 3C1 * 2C1 = 24 ways
So 6, 9, 12, 18, 8, 12. 16, 24 ways - options in the question are 10, 16 and 18
So 16 and 18 are possible ways.
Option D
This can be done if he receives;
3 shirts, 2 ties, 1 jacket(s) or
3 shirts, 3 ties, 1 jacket(s) or
3 shirts, 2 ties, 2 jacket(s) or
3 shirts, 3 ties, 2 jacket(s) or
4 shirts, 2 ties, 1 jacket(s) or
4 shirts, 3 ties, 1 jacket(s) or
4 shirts, 2 ties, 2 jacket(s) or
4 shirts, 3 ties, 2 jacket
We have to find out combinations for each set(have to pick 1 from each shirt, tie and jacket) and match from questions-
So 3 shirts, 2 ties, 1 jacket(s) = 3C1 * 2C1 * 1C1 = 6 ways
3 shirts, 3 ties, 1 jacket(s) = 3C1 * 3C1 * 1C1 = 9 ways
3 shirts, 2 ties, 2 jacket(s) = 3C1 * 2C1 * 2C1 = 12 ways
3 shirts, 3 ties, 2 jacket(s) = 3C1 * 3C1 * 2C1 = 18 ways
4 shirts, 2 ties, 1 jacket(s) = 4C1 * 2C1 * 1C1 = 8 ways
4 shirts, 3 ties, 1 jacket(s) = 4C1 * 3C1 * 1C1 = 12 ways
4 shirts, 2 ties, 2 jacket(s) = 4C1 * 2C1 * 2C1 = 16 ways
4 shirts, 3 ties, 2 jacket(s) = 4C1 * 3C1 * 2C1 = 24 ways
So 6, 9, 12, 18, 8, 12. 16, 24 ways - options in the question are 10, 16 and 18
So 16 and 18 are possible ways.
Option D
