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10 May 2021, 07:35
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
47% (01:59) correct
53%
(01:52)
wrong
based on 206
sessions
History
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Time
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There are two models of cars, A and B. Model A has 4 color variants Red, Blue, Green, and Yellow. Model B also has 4 color variants Red, Blue, Green, and Yellow. In how many ways can Chelsea choose three cars such that all three cars are of different colors?
A. 16
B. 24
C. 32
D. 96
E. 192
A. 16
B. 24
C. 32
D. 96
E. 192
10 May 2021, 19:20
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RakshithTN
Given: Model A has 4 color variants Red, Blue, Green, and Yellow. Model B also has 4 color variants Red, Blue, Green, and Yellow.
Ways in which Chelsea can choose 3 cars of different colors =?
i. Possibilities of picking all 3 Model A cars = 4C3 = 4
ii. Possibilities of picking all 3 Model B cars = 4C3 = 4
iii. Possibilities of picking 2 Model A cars and 1 Model B car = 4C2 * 2C1 = 12 [after selecting Model A, only two colors will be left in Model B]
iv. Possibilities of picking 2 Model B cars and 1 Model A car = 4C2 * 2C1 = 12 [after selecting Model B, only two colors will be left in Model A]
Total ways/possibilities = 4 + 4 + 12 + 12 = 32 ways.
So, correct answer is option C.
05 Jan 2024, 06:48
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Three cars can be selected as follows:
AAB ABB AAA BBB
Three different colors can be selected 4!/3! = 4 ways
Three colors can be assigned as follows:
AAB: 3!/2! = 3 ways
ABB: 3!/2! = 3 ways
AAA: 3!/3! = 1 way
BBB: 3!/3! = 1 way
Total ways colors can be assigned: 3+3+1+1 = 8
Total ways cars can be selected:
4*8 = 32
Posted from my mobile device
AAB ABB AAA BBB
Three different colors can be selected 4!/3! = 4 ways
Three colors can be assigned as follows:
AAB: 3!/2! = 3 ways
ABB: 3!/2! = 3 ways
AAA: 3!/3! = 1 way
BBB: 3!/3! = 1 way
Total ways colors can be assigned: 3+3+1+1 = 8
Total ways cars can be selected:
4*8 = 32
Posted from my mobile device
