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27 Jan 2025, 02:51
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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:
52% (02:28) correct
48%
(02:47)
wrong
based on 62
sessions
History
Date
Time
Result
Not Attempted Yet
Five T-shirts – Red, Blue, Yellow, Green and Orange need to be distributed among 8 children such that any child gets at most 2 T-shirts. In how many different ways can this be done?
A. \(2 * 3^2 * 7 * 11\)
D. \(2^2 * 3 * 5 * 7 * 11\)
E. \(2^3 * 3^3 * 5 * 7 * 17\)
A. \(2 * 3^2 * 7 * 11\)
B. \(2^2 * 3 * 5 * 11\)
C. \(2^4 * 3 * 5 * 7 * 17\)D. \(2^2 * 3 * 5 * 7 * 11\)
E. \(2^3 * 3^3 * 5 * 7 * 17\)
27 Jan 2025, 03:35
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There are 3 ways 5 T-shirts can be split amongst 8 children such that any child gets at most 2 T-shirts
2 2 1
2 1 1 1
1 1 1 1 1
For 2 2 1
Select 3 children who get T-shirts = 8C3 = 8*7
These T-shirts can be distribute amongst 3 children in 3!/2! ways = 3 ways
Selecting the T-shirts = 5C2 * 3C2 * 1 = 10*3
Total no. of ways for this case = 8*7*3*10*3
For 2 1 1 1
Select 4 children who get T-shirts = 8C4 = 7*2*5
These T-shirts can be distribute amongst 4 children in 4!/3! ways = 4 ways
Selecting the T-shirts = 5C2 * 3C1 * 2C1 * 1
Total no. of ways for this case = 7*2*5*4*10*3*2
For 1 1 1 1 1
Select 5 children who get T-shirts = 8C5 = 8*7
Selecting the T-shirts = 5*4*3*2*1
Total no. of ways for this case = 8*7*5*4*3*2
Now to find overall no. of ways, we'll add all 3 cases
\((8*7*3*10*3) + (7*2*5*4*10*3*2) + (8*7*5*4*3*2)\)
=> \(8*7*3*10*(3+10+4) = 8*7*3*10*17\)
=> \(2^4 * 3 * 5 * 7 * 17\)
Answer C.
2 2 1
2 1 1 1
1 1 1 1 1
For 2 2 1
Select 3 children who get T-shirts = 8C3 = 8*7
These T-shirts can be distribute amongst 3 children in 3!/2! ways = 3 ways
Selecting the T-shirts = 5C2 * 3C2 * 1 = 10*3
Total no. of ways for this case = 8*7*3*10*3
For 2 1 1 1
Select 4 children who get T-shirts = 8C4 = 7*2*5
These T-shirts can be distribute amongst 4 children in 4!/3! ways = 4 ways
Selecting the T-shirts = 5C2 * 3C1 * 2C1 * 1
Total no. of ways for this case = 7*2*5*4*10*3*2
For 1 1 1 1 1
Select 5 children who get T-shirts = 8C5 = 8*7
Selecting the T-shirts = 5*4*3*2*1
Total no. of ways for this case = 8*7*5*4*3*2
Now to find overall no. of ways, we'll add all 3 cases
\((8*7*3*10*3) + (7*2*5*4*10*3*2) + (8*7*5*4*3*2)\)
=> \(8*7*3*10*(3+10+4) = 8*7*3*10*17\)
=> \(2^4 * 3 * 5 * 7 * 17\)
Answer C.
General Discussion
07 Jul 2026, 01:14
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