Leila is putting 12 colored light bulbs into a string of lights. There are 6 orange light bulbs, 2 blue light bulbs, and 4 green light bulbs. How many distinct orders of light bulbs are there if two light bulbs of the same color are considered identical (not distinct)?

Pablo is putting 12 colored light bulbs into a string of lights. There are 3 pink light bulbs, 6 blue light bulbs, and 3 red light bulbs. How many distinct orders of light bulbs are there if two light bulbs of the same color are considered identical (not distinct)?

Hans is putting 11 colored light bulbs into a string of lights. There are 3 blue light bulbs, 4 red light bulbs, and 4 white light bulbs. How many distinct orders of light bulbs are there if two light bulbs of the same color are considered identical (not distinct)?

A sales assistant is hanging 12 sweaters on a rack. He has 5 purple sweaters, 5 pink sweaters, and 2 gray sweaters. In how many distinct orders can the sweaters be arranged if two sweaters of the same color are considered identical (not distinct)?

Mai is arranging 12 cans of food in a row on a shelf. She has 5 cans of peas, 1 can of corn, and 6 cans of beets. In how many distinct orders can the cans be arranged if two cans of the same food are considered identical (not distinct)?

Suppose we want to choose 6 colors, without replacement, from 11 distinct colors.(If necessary, consult a list of formulas.)(a) How many ways can this be done, if the order of the choices matters?(b) How many ways can this be done, if the order of the choices does not matter?