Question 76805
How many different 5-card hands can be dealt from a standard deck of 52 cards?
This is a combination because
1 repititons are not allowed
2 order is NOT important
C(n,r)={{{highlight(n!/(r!(n-r)!))}}}
n=52 r=5
C(52,5)={{{52!/(5!(52-5)!)}}}
={{{52!/(5!*47!)}}}
={{{52*51*50*49*48*47!/(5!*47!)}}}
{{{52*51*50*49*48*cross(47!)/(5!*cross(47!))}}}
{{{52*51*50*49*48/(5*4*3*2*1)}}}
{{{52*51*(5*2*5)*49*(4*3*4)/(5*4*3*2*1)}}}
{{{52*51*cross(5*2)*5*49*cross(4*3)*4/cross(5*4*3*2*1)}}}
{{{52*51*5*49*4}}}
C(52,5)={{{highlight(2598960)}}}
The TI-83-84 calculators have the combination feature under the MATH key all the way to the right is PRB, nCr is the third option down.
Type 52 nCr 5 hit enter and it gives you 2598960, it depends on how much work your teacher wants to see as to whether you can use that kind of feature.
Happy Calculating!!!