How many different four digit numbers can be made from the digits 1 through 7 if no digit is repeated

7!/4!3!

Hmmm. Is it not 7P4 = 7!/3! ?

number of such numbers

= 7x6x5x4
= 7!/3!
= P(7,3)
= 210 , as Steve stated

To find the number of different four-digit numbers that can be made from the digits 1 through 7 without repetition, we can use the concept of permutations.

A permutation is an arrangement of objects in a specific order. In this case, we want to arrange the digits 1 through 7 to form four-digit numbers.

To find the number of permutations, we can use the formula for arrangements of objects without repetition:

P(n, r) = n! / (n-r)!

Where "n" represents the total number of objects (7 in this case) and "r" represents the number of objects we want to arrange (4 in this case). The exclamation mark denotes the factorial of a number.

Using this formula, we can calculate the number of different four-digit numbers as follows:

P(7, 4) = 7! / (7-4)!
= 7! / 3!
= (7)(6)(5)(4) / (3)(2)(1)
= 840 / 6
= 140

Therefore, there are 140 different four-digit numbers that can be made from the digits 1 through 7 without repetition.