At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are to be elec - Mathematics MCQ AIEEE 2006 2026 | ExamTest.live

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At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are to be elected. If a voter votes for at least one candidate, then the number of ways in which he can vote is:

Solution & Step-by-step Explanation

The voter can choose 1, 2, 3, or 4 candidates out of 10 .Number of ways =^{10} C_{1} +^{10} C_{2} +^{10} C_{3} +^{10} C_{4}^{10} C_{1} = 10^{10} C_{2} = \frac{10 \times 9}{2} = 45^{10} C_{3} = \frac{10 \times 9 \times 8}{3 \times 2 \times 1} = 120^{10} C_{4} = \frac{10 \times 9 \times 8 \times 7}{4 \times 3 \times 2 \times 1} = 210 Total ways = 10 + 45 + 120 + 210 = 385 .

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At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are to be elected. If a voter votes for at least one candidate, then the number of ways in which he can vote is:

5040

6210

385

1110

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