Let c(n, k) = the number of k-membered subsets of an n-membered set. find (a) c(6, k) for k = 0,1, (b) c(7, k) for k = 0,1.

(a) , , , , , , .

(b) , , , , , , , .

Step-by-step explanation:

In this exercise we only need to recall the formula for C(n,k):

where the symbol is the factorial and means

.

By convention 0!=1. The most important property of the factorial is , for example 3!=1*2*3=6.

(a) The explanations to the solutions is just the calculations.

(b) The explanations to the solutions is just the calculations.

For all the calculations just recall that 4! =24 and 5!=120.

1. sometimes

2.   never

3   .08c = 7.50+.05c   250 pages

step-by-step explanation:

1.   sometimes

the theoretical probability of rolling a 1 is 1/6.   perhaps you got really lucky and never rolled a 1   in those 60 times.   your experimental probability is 0.   or perhaps you rolled a 1   20 times.   your experimental probability is 20/60 is 1/3.     it really just depends on how you rolled in that experiment.

2.   never

the probability of the event occurring is 1.   that is being 100 % sure it will happen.   that is the maximum amount of confidence we have.

3.   no customer card cost:   .08 times number of pages

customer card cost:   7.50 + .05 times number of pages

we want to find when it costs the same amount, so we will set these equal

let c = number of pages

.08c = 7.50+.05c

subtract .05c from each side

.08c-.05c = 7.5+.05c-.05c

.03c=7.5

divide each side by .03

.03c/.03 = 7.5/03

c =250  

the cost is the same at 250 pages

my guess is

step-by-step explanation: