help in mathpz

Test Preparation SAT Preparation
1

<p>Philip is on a committee that has 6 members. How many different subcommittees of 3 can he forme that have philip in them?
a)3
b)6
c)10
d)15
e)20</p>

<p>what is the greatest number of balls of radius 1 in that will fit into a covered wooden box with interior dimensions of 2in by 4in by 4 in?</p>

<p>a)2
b)4
c)8
d)16
e) 32</p>

<p>ten distinct lines lie in the same plane. No pair of these lines is parallel o each other, and no more than 2 of these lines intersect at any one point. How many points lie on more than one of these lines?</p>

<p>a)10
b)36
c)45
d)55
e)100</p>

2

<p>For the first one we are forced to choose Philip. We then choose 2 from the remaining 5 members. So the answer is 5C2 = 10, choice (C).</p>

3

<p>For the second one, if the radius of a ball is 1, then its diameter is 2. So the number of such balls that will fit is the same as the number of cubes of side length 2 that will fit. Now we just divide volumes: (2<em>4</em>4)/(2<em>2</em>2) = 4, choice (B).</p>

4

<p>Thanks. But (okay the most cliche question of all :P) why can’t we put 5*4= 20 in the first one 5(the number of possibilities for the 2nd member) and 4 (the number of possibilities of the 3rd member i.e. 6-(philip)-(the 2nd member). I don’t think there will be repeated members then yet it doesn’t get the same answer as 5C2…
It’s always been confusing for me O.o</p>

5

<p>We can think of your mistake in a few different ways</p>

<p>(1) You are counting Philip and Fred as different from Fred and Philip. But that’s the same committee. In other words, if you compute 5*4 you’ve counted each committee twice. So you need to divide by 2.</p>

<p>(2) 5P2 =5<em>4 counts the number of permutations or arrangements. But we want the number of UNORDERED groups. This is 5C2= 5</em>4/2.</p>

6

<p>ahaaa… yeah i realized
this has always confused me no matter what </p>

<p>what abt #3?!</p>

<p>anyone?!!?!
(with detailed explanation plx :frowning: )</p>

7

<h1>3) We are counting the number of ways to choose 2 of the lines from the 10. So the answer is 10C2 = 45, choice (C)</h1>

8

<p>yeah ohkaayyy…</p>

<p>another question:</p>

<p>If f(2x+3)=4x-7 for all values of x, for what value of t is f(t)=1</p>

<p>a)2 b)3 c)5 d)7 e)10</p>

9

<p>the answer for post #8 is d</p>