<p>I need someone to explain these 2 problems to me. </p>
<p>First one:
</a></p>
<p>The answer is suppose to be 72</p>
<p>Second one:
</a></p>
<p>The answer is suppose to be .5</p>
<p>Here’s a hint. </p>
<p>How many possibilities of arranging five cards are there? </p>
<p>5<em>4</em>3<em>2</em>1 or 120.</p>
<p>How many possibilities are there to have the restricted card in position 1? </p>
<p>4<em>3</em>2*1 or 24. </p>
<p>Now you have one more step to go through. If that makes no sense, review the permutations and combinations rules.</p>
<p>Thanks, that helped. I understand that one now. Can anyone explain the second one?</p>
<p>
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<p>Check the vertical line. If one part of the line (QS) is equivalent to 1/3 of the entire line (QV), the remaining part (SV) must be 2/3. </p>
<p>Since you compare fractions, you do not need to use the precise 1/2<em>b</em>h formula twice, you can simply compare the b*h of both triangles. The trick here is to make the value of the larger triangle equal to 1. </p>
<p>The fraction will then be 2/3 * 3/4 over 1. Or 6/12 or .5. </p>
<p>But to keep it easier to follow, we will also use the area formulae. </p>
<p>Area 1 = 1/2 * 2/3 * 3/4 = 1/4 </p>
<p>Area 2 = 1/2 *1 * 1 = 1/2 </p>
<p>Answer is 1/4 over 1/2 or .5.</p>
<p>Oh okay! I was overthinking the problem at first. Thanks!</p>
<p>I think that there is a simpler and more intuitive approach to problem 1.</p>
<p>Start with the restricted card. It can’t be at either end. So there are 3 possible positions for the restricted card. Place it.</p>
<p>Then with the restricted card placed. Pick another card. There are 4 remaining slots for that.
And another card. There are 3 remaining slots for that.
And another card. There are 2 remaining slots for that.
And the last card. Just one slot.</p>
<p>Multiply it out: 3x4x3x2x1 = 72 possibilities</p>
<p>yea, i agree with fogcity</p>