Answer:
146 didn't vote
Step-by-step explanation:
With this situation, start from the vote for all 4, then move onto the vote of 3 out of 4, then the vote of 2 of the 4 and lastly deal with with the vote of 1 out of the 4;
I've tabulated it in the attached excel document;
First, there are 50 votes for A, B, C and D;
Then there are 100 votes for B, C and D;
Now, the 50 who voted for all 4 are included in the 100 for B, C and D because someone who votes for A, B, C and D has voted for B, C and D;
This means we need to deduct 50 from 100 to get 50, which is the number of voters who voted for B, C and D, but not A;
This is done for all the options where students voted for 3 of the 4;
For those who voted C and D, there are 250, but this will include the 50 who voted A, C and D, the 50 who voted B, C and D and the 50 who voted A, B, C and D;
So, we have to subtract 3×50 (= 150) from 250 to get 100 as is shown in the table;
The table is quite helpful as it shows clearly who will be included in the numbers given in the question info;
We do the same for all those who vote for 2 of the 4;
For those who voted just D, we need to add the votes of all those who voted for D and anyone else, which is 500, and subtract this from the total number of votes for D, which is 1000;
And similarly, we do the same for A, B and C as well;
Now, we can sum all the votes, which gives 2850 and subtract this from the total number of voters, which is 2996 (remember we have to exclude the 4 band members as they can't vote);
This gives us:
2996 - 2850 = 146
