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)?

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)?

A set of 12 books has 3 identical Quant books, 3 identical Reasoning books, 4 identical English books and 2 different books on General Awareness. In how many different ways can these 12 books be arranged in a book-shelf?

Find the number of distinct arrangements of the 12 letters in REENGINEERED.Two of the same letter are considered identical (not distinct).

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)?