JEE MAIN - Mathematics (2006 - No. 21)
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 of be selected, if a voter votes for at least one candidate, then the number of ways in which he can vote is
5040
6210
385
1110
Vysvetlenie
A voter can give vote to either 1 candidate or 2 candidates or 3 candidates or 4 candidates.
Case 1 : When he give vote to only 1 candidate then no ways = $${}^{10}{C_1}$$
Case 2 : When he give vote to 2 candidates then no ways = $${}^{10}{C_2}$$
Case 3 : When he give vote to 3 candidates then no ways = $${}^{10}{C_3}$$
Case 4 : When he give vote to 4 candidates then no ways = $${}^{10}{C_4}$$
So, total no of ways he can give votes
= $${}^{10}{C_1} + {}^{10}{C_2} + {}^{10}{C_3} + {}^{10}{C_4}$$
= 385
Note : Here we use addition rule as he can vote any one of those four rules. Whenever there is "or" choices, we use addition rule.
Case 1 : When he give vote to only 1 candidate then no ways = $${}^{10}{C_1}$$
Case 2 : When he give vote to 2 candidates then no ways = $${}^{10}{C_2}$$
Case 3 : When he give vote to 3 candidates then no ways = $${}^{10}{C_3}$$
Case 4 : When he give vote to 4 candidates then no ways = $${}^{10}{C_4}$$
So, total no of ways he can give votes
= $${}^{10}{C_1} + {}^{10}{C_2} + {}^{10}{C_3} + {}^{10}{C_4}$$
= 385
Note : Here we use addition rule as he can vote any one of those four rules. Whenever there is "or" choices, we use addition rule.