Discrete structures please solve

2. (3 mands) Use the Binomial Theoren to calculate C(n,0)2C(n,)+4C(n,2)c(nx)++ (1)n245(n,n), for any positive integer n. 3. (4 marks) A bagel shop has onion bagels, poppy seed bagels, salty bagels, pumpernickel bag sesame seed bagels, raisin bagels and plain bagels. How many ways are there to choose a) 10 bagels? b) 10 bagels with at least one of each kind? c) 10 bagels with exactly three raisin bagels and no more than two salty bagels? Explain your answers