How many 5-digit license plates can be make using the digits 1,2,3,4,5,6,7 if an odd digit must come first and repetitions are allowed? what if repetitions are not allowed

Repetitions allowed  9,604      

Step-by-step explanation:

First digit: {1, 3, 5, or 7} = 4 choices

2nd digit: {1, 2, 3, 4, 5, 6, or 7} = 7 choices

3rd digit: {1, 2, 3, 4, 5, 6, or 7} = 7 choices

4th digit: {1, 2, 3, 4, 5, 6, or 7} = 7 choices

5th digit: {1, 2, 3, 4, 5, 6, or 7} = 7 choices

1st digit and 2nd digit and 3rd digit and 4th digit and 5th digit

    4        x           7         x         7          x        7         x         7

= 4(7)⁴

= 9,604

Repetitions not allowed    1,440    

Step-by-step explanation:

First digit: {1, 3, 5, or 7} = 4 choices

2nd digit: {1, 2, 3, 4, 5, 6, or 7} - {1st digit} = 7 - 1 = 6 choices

3rd digit: {1, 2, 3, 4, 5, 6, or 7} - (1st & 2nd digits} = 7-2 = 5 choices

4th digit: {1, 2, 3, 4, 5, 6, or 7} - {1st, 2nd, & 3rd digits} = 7-3 = 4 choices

5th digit: {1, 2, 3, 4, 5, 6, or 7} - (1st, 2nd, 3rd, & 4th digits} = 7-4 = 3 choices

1st digit and 2nd digit and 3rd digit and 4th digit and 5th digit

    4        x           6         x         5          x        4         x         3

= 1,440

final answer is : )

26

step-by-step explanation: