Counting > With or without repeating
1234With or without repeating

Theory

There are 104 options when choosing 4 elements out of 10 available elements and repetitions are permitted.

When choosing 4 elements out of 10 available elements and repititions are not permitted there are 10 × 9 × 8 × 7 options. This is called the number of permutations of 4 out of 10 elements.

When repetition is not permitted, you get a multiplication of a series of decreasing successive numbers. The multiplication of the decreasing series of numbers 10 through 1 is called 10 factorial.

You write this as 10!, so 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 .

It has been agreed that 0 ! = 1 . The calculator has a function that calculates factorials.

When dealing with permutations you also encounter a decreasing series of numbers. This series, however, does not always end with the number 1.
Your calculator has a special function to calculate permutations like 10 9 8 7 = 5040 .

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