Answer:
a) 110,880
b) 8.61x10^37
c) 7.18x10^19
Step-by-step explanation:
To find the amount of options, use the following combination equation.
n!/[r! * (n - r)]
In this equation, n represents the amount of possible options and r represents the amount being chosen at a time. We can now calculate out the answer for each possibility.
a) In this case, n would equal 12 and r would equal 6.
n!/[r! * (n - r)]
12!/[6! * (12 - 6)]
479001600/[720*6]
479001600/4320
110,880
b) In this case, n would equal 36 and r would equal 6
n!/[r! * (n - r)]
36!/[6! * (12 - 6)]
3.72x10^41/[720*6]
3.72x10^41/4320
8.61x10^37
c) For this one, n would equal 24 and r would equal 6. We would also then have to divide the answer at the end by 2.
n!/[r! * (n - r)]
12!/[6! * (12 - 6)]
6.20x10^23/[720*6]
6.20x10^23/4320
1.44x10^20 ÷ 2 = 7.18x10^19
