After testing asphalt shingles are classified as high medium

After testing, asphalt shingles are classified as high, medium, or low grade, and different grade shingles are sold under different warranties. In how many ways can the next 15 shingles be classified into high, medium, or low grade? How many classifications have three, five, and seven shingles in the high, medium, and low grade categories, respectively? If the classifications are all equally likely, what is the probability of the event in part (b)? The binomial theorem states that (a + b)^n = summation_k=0^n (n k) a^k b^n-k. Use the binomial theorem to show that summation_k=0^n (n k) = 2^n.

Solution

a) 15C3 = 455

b)

3C3 = 1

5C3 = 10

7C3 =35

b)

probabilities

for 3 -----1

for 5------ 1/10

for 7 ------1/35

for the other question

i can gladly help you but you should post it in a new question