Question 1092321: at an election there are 5 candidates and 3 members are to be elected. a voter is entitled to vote for any number of candidates not greater than the numbers to be elected.the number of ways a voter choose to vote is
Answer by greenestamps(13216)   (Show Source):
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The voter can choose 0 of the 5 candidates in C(5,0) ("5 choose 0") ways.
The voter can choose 1 of the 5 candidates in C(5,1) ways.
The voter can choose 2 of the 5 candidates in C(5,1) ways.
The voter can choose 3 of the 5 candidates in C(5,3) ways.
The voter is not allowed to choose more than 3 of the 5 candidates.
The easiest way to find the total number of ways the voter can choose is to be familiar with Pascal's triangle, whose entries are the C(n,r) numbers. The 5th row of Pascal's triangle is
1 5 10 10 5 1
Those numbers are the numbers of ways the voter can choose 0, 1, 2, 3, 4, or all 5 of the 5 candidates. So the number of ways the voter can choose up to 3 of the candidates is
1+5+10+10 = 26
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