Space shuttle astronauts each consume an average of 3000 cal

Space shuttle astronauts each consume an average of 3000 calories per day. One meal normally consists of a main dish, a vegetable dish, and two different desserts. The astronauts can choose from 1010 main dishes, 77 vegetable dishes, and 1414 desserts. How many different meals are possible?

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Solution

He can choose 1 main dish in 10C1 ways

He can choose 1 veg dish in 8C1 ways

He can choose 2 deserts in 13C2 ways

since all these events are independent of other

Hence number of ways = 8C1 * 10C1 * 13C2 = 8 * 10 * 13 * 12 / 2 -= 6240 ways