Question 1066088
Part a)

Since it appears that the order does not matter (we are just choosing any 5 at once), then we are using a combination. A couple of different ways to compute this.

You can use the nCr button on your calculator, but I will do it using the formula.

So  nCr  = {{{n!/((n-r)!* r!)}}}

We are finding 10 C 5 =   {{{ 10! /(5! * 5!) }}}

10! is quite large, so let's try to do some simplification.

{{{(10*9*8*7*6*5*4*3*2*1)/((5*4*3*2*1)*(5*4*3*2*1))}}}

{{{(10*9*8*7*6*cross(5)*cross(4)*cross(3)*cross(2)*cross(1))/((cross(5)*cross(4)*cross(3)*cross(2)*cross(1))*(5*4*3*2*1))}}}

{{{(10*9*8*7*6)/(5*4*3*2*1)}}}

{{{(cross(10)*9*8*7*6)/(cross(5)*4*3*cross(2)*1)}}}

{{{(9*8*7*6)/(4*3)}}}

{{{(cross(9)3*cross(8)2*7*6)/(cross(4)*cross(3))}}}

and 3 * 2* 7 * 6  is  {{{highlight(252)}}}.

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Part b)

10 is fixed so we really only have  9 questions and we are choosing 4.

So  9 C 4 = 

{{{(9*8*7*6*5*4*3*2*1)/((5*4*3*2*1)(4*3*2*1))}}}

{{{(9*8*7*6)/(4*3*2*1)}}}

{{{(cross(9)3*cross(8)*7*6)/(cross(4)*cross(3)*cross(2)*cross(1))}}}

So 3 * 7 * 6 =  {{{highlight(126)}}}

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Finally, Google will do it for you as well.

10 choose 5 : https://www.google.com/#q=10+choose+5

9 choose 4 : https://www.google.com/#q=9+choose+4