If no digits may be used more than once , how many 5 digits can be formed using only the digits 3, 8,1,2,5 ,7?
that is just the number of permutations of 5 things out of 6: 6P5 = 6!/1!
Why is there an exclamation point though?
To find out how many 5-digit numbers can be formed using the digits 3, 8, 1, 2, 5, and 7 without repeating any digit, we can use the concept of permutations.
The number of ways to arrange a set of n objects is given by n!. However, in this case, since we are forming a 5-digit number, we need to consider the number of objects we have and the number of slots to fill.
In the first slot, we have 6 choices (6 digits available). After placing a digit in the first slot, there are only 5 remaining digits to choose from for the second slot. Continuing this pattern, we have 4 choices for the third slot, 3 choices for the fourth slot, and 2 choices for the fifth slot.
Therefore, the total number of 5-digit numbers that can be formed without repeating any digit is:
6 * 5 * 4 * 3 * 2 = 720
So, using the digits 3, 8, 1, 2, 5, and 7, we can form 720 different 5-digit numbers without repeating any digit.