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why cant it be 8C4=70
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purvibagmar
A purse contains 3 quarters, 3 dimes and 2 nickels. How many different possible sets of 4 coins could be selected from the purse?

A. 6
B. 8
C. 9
D. 10
E. 18

why cant it be 8C4=70
­
The combination formula 8C4 = 70 calculates 4-coin groups from 8 coins, assuming all coins are distinguishable. However, in this question, quarters, dimes, and nickels are considered indistinguishable from each other. For example, (Q1, Q2, D1, D2) is the same group as (Q1, Q3, D1, D2). 
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We have 4 coins to select.
3Q, 3D and 2N

1. Say we select all 3Q:

QQQD
QQQN
=2 ways

2. Say we select 2Q:
QQDD
QQNN
QQDN
=3 ways

3. Say we select 1Q:
QDDD
QDDN
QDNN
=3 ways

4. Say we select 0Q:
DDDN
DDNN
=2 ways

Total=3Q+2Q+1Q+0Q
=2+3+3+2
=10 ways
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here since the numbers are small we can do it manually, but how to solve this in a more traditional approach because I want to be prepared incase numbers are huge?
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