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Gabriel's favorite snack just became available in 3 new flavors, and he wants to try each of the new flavors one after the other. In how many unique orders can Gabriel arrange the new flavors?

Gabriel's favorite snack just became available in 33 new flavors, and he wants to try each of the new flavors one after the other.\newlineIn how many unique orders can Gabriel arrange the new flavors?

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Full solution

Q. Gabriel's favorite snack just became available in 33 new flavors, and he wants to try each of the new flavors one after the other.\newlineIn how many unique orders can Gabriel arrange the new flavors?
  1. Number of New Flavors: List the number of new flavors: There are 33 new flavors that Gabriel wants to try.\newlineTo find out the number of unique orders in which he can arrange these flavors, we need to calculate the number of permutations of these 33 items.\newlineNumber of unique orders: 3!3!
  2. Calculating Permutations: Calculate the value of 3!3!.
    Number of unique orders = 3!3!
    = 3×2×13 \times 2 \times 1
    = 66

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