SOLUTION: 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 numbe
Algebra.Com
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): You can put this solution on YOUR website!
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
RELATED QUESTIONS
Respected Sir,
Please help me to simplify this question :
At an election there are 5... (answered by sudhanshu_kmr)
A weighted voting is an electoral system in which the voters do not have the same amount... (answered by ikleyn)
The city of Raleigh has 10400 registered voters. There are two candidates for city... (answered by ikleyn)
In an engineering college committee, a president needs to be elected out of 15 eligible... (answered by stanbon)
There are 75 people present to vote new members into their organization. There are 12... (answered by stanbon)
5! is read_____________________________________________
Its value is... (answered by stanbon)
A local election will be held with 12 candidates running for a new county governing... (answered by ikleyn)
Club members are going to elect their officers. If there are four candidates for... (answered by math_tutor2020,ikleyn)
The city of Raleigh has 10400 registered voters. There are two candidates for city... (answered by Boreal)