Kelly has different books to arrange on a​ shelf; 4 ​blue, 2 ​green, and 3red. Answer parts a through e below. ​(a) In how many ways can the books be arranged on a​ shelf?     ​(b) If books of the same color are to be grouped​ together, how many arrangements are​ possible?   ​(c) In how many distinguishable ways can the books be arranged if books of the same color are identical but need not be grouped together.

please answer the question in the photo. Thank you

Jessica is grocery shopping and has 16 cherry tomatoes and 12 grape tomatoes in her shopping basket. When she gets home, she prepares her ingredients for lunch, but she forgets which of the tomatoes are cherry and which are grape. She cannot distinguish between the two types of tomatoes, so she just picks 13 tomatoes. How many different sets of 13 tomatoes are possible if there are exactly 7 cherry tomatoes?

A jar of jellybeans has three different colors of jellybeans:  green,  red, and yellow. Let’s use symbols to represent each color: green = g, red = r, and yellow = y. If you choose a handful of four jellybeans from the jar, how many different combinations of jellybeans are possible? Assume there are at least four of each color.