> 100 people were polled to check which of 3 music categories they liked:
> 63 checked R&R
> 44 checked RAP
> 24 checked JAZZ
> -----------------------------------------------------------------------
> --------------------------
> 3 checked all 3 categories.
> 25 of those that checked R&R also checked RAP but not JAZZ.
> 5 of those that checked RAP also checked JAZZ but not R&R.
> 14 of those that checked JAZZ also checked R&R but not RAP.
>
> How many people checked NONE of the 3 categories?
3 people checked all 3 choices. Of the rest that checked at least 1
choice we are left with:
60 that checked R&R
41 that checked RAP
21 that checked JAZZ
Of those that checked 2 choices we have:
25 that checked R&R and RAP
5 that checked RAP and JAZZ
14 that checked JAZZ and R&R
Thus:
39 R&Rers (25+14) made 2 choices leaving 21 that made but 1 choice
30 RAPers (25+5) made 2 choices leaving 11 that made 1 choice
19 JAZZers (14+5) made 2 choices leaving 2 that made 1 choice
Summarizing:
The number making 1 choice was (21+11+2) ..........34
The number making 2 choices was (25+14+5) ........44
The number making 3 choices was (as stated) ...........3
------------------------------------------------------------------------
----
The total of those making at least 1 choice was thus 81
Thus 19 of the people polled checked NONE of the categories.
FW
"Am I not destroying my enemies when I make friends of them?"
- Abraham Lincoln
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