Question 667346
The formula for combinations is generally {{{26C5=n! / (r! (n - r)!)}}}, where{{{ n}}} is the total number of possibilities to start and {{{r}}} is the number of selections made. 

In our example, we have 26 people; therefore, {{{n = 26}}}. 

We want to select {{{5}}} youngest people, so {{{r = 5}}}}.


{{{26! / (5!(26 - 5)!)}}}

{{{26! / (5! (21)!)}}}

{{{(26*25*24*23*22*21*20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1) / (5*4*3*2*1 (21*20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1))}}}

{{{(26*25*24*23*22*(cross(21*20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*cross5*4*3*2*1))) / (5*4*3*2*1 (cross(21*20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4*3*2*1)))}}}


{{{(26*cross(25)5*cross(24)cross(6)cross(2)*23*22) / (cross(5)*cross(4)*cross(3)*cross(2)*1)}}}


{{{26*5*23*22= 65780 }}}


if there are exactly {{{5}}} youngest people and if they were all selected, the probability is
{{{5/26C5 = 5/65780=0.000076011}}}