adeline has 4 numbers 1, 5, 0, 7 how many numbers can she makes?

Case I : 1-digit numbers
1 digit numbers: 1, 5, 0, 7
No. of 1-digit numbers = 4

Case II: 2-digit numbers
The tens digit must not be zero, and could be one digit out of 1, 5, and 7. Then, the units digit could be one of the rest 3 digits.
No. of 2-digit numbers = 3 × 3 = 9

Case III: 3-digit numbers
The hundreds digit must not be zero, and could be one digit out of 1, 5, and 7. Then, the tens digit could be one of the rest 3 digits. At last, the units digit could be one of the rest 2 digits.
No. of 3-digit numbers = 3 × 3 × 2 = 18

Case IV: 4-digit numbers
The thousands digit must not be zero, and could be one digit out of 1, 5 and 7. Then, the hundreds digit could be one the rest 3 digits. Then, the tens digits could be one of the rest 2 digits. At least, fill the units digit with the last digit.
No. of 4-digit numbers = 3 × 3 × 2 × 1 = 18

Total number of numbers = 4 + 9 + 18 + 18 = 49

assuming that repitition of a digit
1 digit: 4 numbers
2 digits: 4(3) = 12 numbers
3 digits: (4)(3)(2) = 24 numbers
4 digits: (4)(3)(2)(1) = 24 numbers

total = 4+12+24+24 = 64 numbers

Adeline has 4 numbers 1, 5, 0, 7. As no conditions are specified, he can have one digit, two digit numbers, three digit numbers and four digit numbers with the condition that 0 can not be a starting digit of any number.
One digit numbers = 3
Two digit numbers=3x3=9
(Three choices for first digit and three choices for second digit)
Three digit numbers=3x3x2=18
(Three choices for first digit and three choices for second digit and two choices for third digit)
Three digit numbers=3x3x2x1=18
(Three choices for first digit and three choices for second digit and two choices for third digit and one choice for fourth digit)
We can add further cases when digits are repeated

The number of ways to arrange n things is n!

You have 4 things. n = 4.