SOLUTION: I asked for assistance on these problems and got incorrect answers. Please help me find the right answers. 1. In how many ways can a committee of 7 be formed if there are 10 dog

Question 419824: I asked for assistance on these problems and got incorrect answers. Please help me find the right answers.
1. In how many ways can a committee of 7 be formed if there are 10 dogs and 15 cats to choose from and the committee must consist of exactly 3 dogs and 4 cats?
The answer is not 35.
2. A survey of 51 pet owners revealed that 24 owned dogs, 28 owned cats, 11 owned turtles, 12 owned both dogs and cats, 7 owned both dogs and turtles, 3 owned both cats and turtles, and 2 owned all three. Find the number of pet owners who owned none of the three lovely animals.
The answer is not 26.
3. Suppose one can move only down or to the right. How many of the routes from A to B pass through C?
There are 5 rows and 7 columns. A is in the upper left corner and B is in the lower right corner. C is located 3 columns over and two rows down starting at A.
A[][][][][][][]
[][][C][][][][]
[][][ ][][][][]
[][][ ][][][][]
[][][][][][][]B
I said 5^7 = 78,125 but this was incorrect. Please help
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
sorry you got lead astray...

1. there are 10C3 ways to select 3 dogs from 10
___ there are 15C4 ways to select 4 cats from 15
___ the number of ways to form the committee is the product of the possible numbers of the two groups
___ 10C3 multiplied by 15C4

2. you have to start with ownership of all three and eliminate duplicate ownership
___ 3 owned c&t , but 2 of those owned all three , so 1 owned only c&t
___ 7 owned d&t , but 2 of those owned all three , so 5 owned only d&t
___ 12 owned d&c , but 2 of those owned all three , so 10 owned only d&c
___ 11 owned t , but 8 owned other pets , so 3 owned only t
___ 28 owned c , but 13 owned other pets , so 15 owned only c
___ 24 owned d , but 17 owned other pets , so 7 owned only d
___ 43 owned one or more pets , so 8 owned none

3. C is 3 over and 2 down from A , so there are 5 steps to get there
___ you can take the steps in any order , but the 3 overs are the same and the 2 downs are the same
___ the number of different routes from A to C is ___ 5! / [(3!)(2!)]
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