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26 Oct 2021, 05:00
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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A bag contains 5 identical red counters, 3 identical blue counters, and 1 green counter. If 3 counters are selected from the bag, how many different possible sets of counters could be selected?
A. 6
B. 7
C. 9
D. 10
E. 27
A. 6
B. 7
C. 9
D. 10
E. 27
21 Nov 2021, 08:45
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3 counters can be distributed among 3 color buckets as follows:
5!/3!2!= 10.
However, this allows for 2 and 3 counters to be allocated to green, where only 1 is available.
Subtract these instances:
2 counters: remaining counter can be distributed 2 ways.
3 counters: 1 way
Total ways: 10-2-1= 7
Since the ways are few, simple counting is viable:
Allocate to the most restrictive color first, green:
G1 B1 R1
G1 B0 R3
G1 B3 R0
Then:
G0 for remaining:
R3 B0
R0 B3
R2 B1
R1 B2
7 ways
Posted from my mobile device
5!/3!2!= 10.
However, this allows for 2 and 3 counters to be allocated to green, where only 1 is available.
Subtract these instances:
2 counters: remaining counter can be distributed 2 ways.
3 counters: 1 way
Total ways: 10-2-1= 7
Since the ways are few, simple counting is viable:
Allocate to the most restrictive color first, green:
G1 B1 R1
G1 B0 R3
G1 B3 R0
Then:
G0 for remaining:
R3 B0
R0 B3
R2 B1
R1 B2
7 ways
Posted from my mobile device
21 Nov 2021, 19:10
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Bunuel
No. of ways for selecting all the 3 counters of same colours = 2 either red or blue
No. of ways of selecting 2 counter of one colour and. 3rd of different colour
= 4 for either red or blue (same colour) , there will be 2 ways for 3rd counter
No. of ways of selecting all 3 counter of different colours = 1
Total ways = 2+4+1 = 7
Posted from my mobile device
