If 6 different colored balls are to be arranged in a row, how many arrangements

If 6 different colored balls are to be arranged in a row, how many arrangements are possible?

If 6 different colored balls are to be arranged in a row, how many arrangements are possible?

Step 1: Understand that we have 6 different colored balls.
Step 2: Realize that we want to arrange these 6 balls in a row.
Step 3: Know that the number of ways to arrange 'n' different items is given by 'n!'.
Step 4: For our case, 'n' is 6 because we have 6 balls.
Step 5: Calculate 6! (which means 6 factorial).
Step 6: 6! = 6 × 5 × 4 × 3 × 2 × 1.
Step 7: Perform the multiplication: 6 × 5 = 30, 30 × 4 = 120, 120 × 3 = 360, 360 × 2 = 720, and 720 × 1 = 720.
Step 8: Conclude that there are 720 different arrangements of the 6 colored balls.

Factorial Arrangements – The question tests the understanding of permutations, specifically how to calculate the number of ways to arrange a set of distinct items using factorial notation.