2. how many unique ways are there to distribute 6 different pieces of candy to 6 children if each child…

2. how many unique ways are there to distribute 6 different pieces of candy to 6 children if each child receives one piece of candy?

2. how many unique ways are there to distribute 6 different pieces of candy to 6 children if each child receives one piece of candy?

Answer

Explanation:

Step1: Identify the problem type

This is a permutation problem where we need to arrange 6 different candies to 6 children (each gets one), which is equivalent to finding the number of permutations of 6 distinct objects. The formula for permutations of ( n ) distinct objects is ( n! ) (n factorial), where ( n! = n\times(n - 1)\times(n - 2)\times\cdots\times1 ).

Step2: Calculate the factorial

For ( n = 6 ), we calculate ( 6! ). ( 6! = 6\times5\times4\times3\times2\times1 ) First, ( 6\times5 = 30 ), then ( 30\times4 = 120 ), then ( 120\times3 = 360 ), then ( 360\times2 = 720 ), then ( 720\times1 = 720 ).

Answer:

720