Hi Theresa,
How many 2 digit numbers that can be formed using 12 without repeating numbers?
The answer is clearly 2. The numbers are 12 and 21.
How many 3 digit numbers that can be formed using 123 without repeating numbers?
Each of the two, 2 digit numbers can be turned into a three digit number by adding the 3 before the two digits, between the two digits or after the two digits. For example 12 generates 312, 132 and 123. Hence there are 3 times as many three digit numbers as two digit numbers. Thus the number of three digit numbers is 3 × 2 = 6.
How many 4 digit numbers that can be formed using 1234 without repeating numbers?
Each of the six, 3 digit numbers can be turned into a four digit number by adding the 4 before the three digits, between the first and second digits, between the second and third digits or after the three digits. Hence there are 4 times as many four digit numbers as three digit numbers.
I hope this helps,
Penny
