Respuesta :
The formula [tex]C(n, r)= \frac{n!}{r!(n-r)!} [/tex], where r! is 1*2*3*...r
is the formula which gives us the total number of ways of forming groups of r objects, out of n objects.
for example, given 10 objects, there are C(10,6) ways of forming groups of 6, out of the 10 objects.
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There are 6 cans of regular cola, and 8 cans of diet cola.
in short, let's use the letters R, for regular, and D for diet cola.
So we have 6 R and 8 D. 14 in total.
There are C(14, 3) many ways of picking 3 cans out of 14, so there are
[tex]\displaystyle{ C(14, 3)= \frac{14!}{3!\cdot11!}= \frac{14\cdot13\cdot12}{3\cdot2}=14\cdot13\cdot2= 364[/tex]
ways of forming groups of 3 cans.
Consider the event "2 cans of regular cola and 1 can of diet cola are selected",
this may happen in C(6, 2)*C(8, 1) many ways, since there are C(6, 2) ways of selecting 2 regular colas out of 6, which can be combined with C(8, 1) ways of selecting 1 diet cola out of 8.
[tex]C(6, 2)\cdot C(8, 1)=\displaystyle{ \frac{6!}{2!4!}\cdot \frac{8!}{1!7!}= \frac{6\cdot5\cdot4!}{2!4!}\cdot8=15\cdot8= 120 [/tex]
P(2 cans of regular cola and 1 can of diet cola)=120/364=0.33
Answer: 0.33
