24
Six ways. Eleven if you ignore commutativity and treat 2+10 as different from 10+2.
There are 26 different letters.There are 10 different numbers.If a letter or number is allowed to repeat in the code:Number of ways to make 3 letters = 26 x 26 x 26 = 17,576Number of ways to make 2 numbers = 10 x 10 = 100Number of ways to make 3 letters and 2 numbers = 17,576 x 100 = 1,757,600Each group of 3 letters and 2 numbers can be arranged in (5 x 4 x 3 x 2) = 120 different ways.So the number of different codes = 1,757,600 x 120 = 210,912,000 .If a letter or number is not allowed to repeat in the code:Number of ways to make 3 letters = 26 x 25 x 24 = 15,600Number of ways to make 2 numbers = 10 x 9 = 90Number of ways to make 3 letters and 2 numbers = 15,600 x 90 = 1,404,000Each group of 3 letters and 2 numbers can be arranged in (5 x 4 x 3 x 2) = 120 different ways.So the number of different codes = 1,404,000 x 120 = 168,480,000 .
If you have 6 different numbers and you are asked "how much different ways of arranging these numbers are there",you could use a factorial.1 times 2 times 3 times 4 times 5 times 6=720 ways.
2. 4 if you include negatives.
Write 2 ways in which whole numbers and decimal numbers are different
24
Six ways. Eleven if you ignore commutativity and treat 2+10 as different from 10+2.
There are 26 different letters.There are 10 different numbers.If a letter or number is allowed to repeat in the code:Number of ways to make 3 letters = 26 x 26 x 26 = 17,576Number of ways to make 2 numbers = 10 x 10 = 100Number of ways to make 3 letters and 2 numbers = 17,576 x 100 = 1,757,600Each group of 3 letters and 2 numbers can be arranged in (5 x 4 x 3 x 2) = 120 different ways.So the number of different codes = 1,757,600 x 120 = 210,912,000 .If a letter or number is not allowed to repeat in the code:Number of ways to make 3 letters = 26 x 25 x 24 = 15,600Number of ways to make 2 numbers = 10 x 9 = 90Number of ways to make 3 letters and 2 numbers = 15,600 x 90 = 1,404,000Each group of 3 letters and 2 numbers can be arranged in (5 x 4 x 3 x 2) = 120 different ways.So the number of different codes = 1,404,000 x 120 = 168,480,000 .
2 x 2 x 2 x 3 x 3 = 72
Any four numbers, in this case 3,4,5 and 6, can be arranged 24 different ways , ie 4 x 3 x 2
If you have 6 different numbers and you are asked "how much different ways of arranging these numbers are there",you could use a factorial.1 times 2 times 3 times 4 times 5 times 6=720 ways.
2. 4 if you include negatives.
none
Three ways. 3 + 37 11 + 29 17 + 23
Only 2
74 can be expressed as the sum of two numbers in different ways, such as 37 + 37, 36 + 38, or 2 + 72.