contestada

How many three-digit numbers can be formed under each condition?
(a) The leading digit cannot be zero.
(b) The leading digit cannot be zero and no repetition of digits is allowed.
(c) The leading digit cannot be zero and the number must be a multiple of 5.
(d) The number is at least 400.

Respuesta :

pedrocarratore

Answer:

(a) 900

(b) 648

(c) 180

(d) 600

Step-by-step explanation:

If there are no restrictions, there are 10 possible values for each digit of a three-digit number.

(a) The leading digit cannot be zero

There are 9 options for the first digit and 10 for the remaining digits.

[tex]n=9*10*10 = 900[/tex]

(b) The leading digit cannot be zero and no repetition of digits is allowed.

[tex]n=9*9*8=648[/tex]

(c) The leading digit cannot be zero and the number must be a multiple of 5.

If a number is a multiple of five, it must end in 0 or 5

[tex]n=9*10*2=180[/tex]

(d) The number is at least 400.

If the number is at least 400, the first digit can only be 4, 5, 6, 7, 8 or 9. There are no restrictions for the remaining digits.

[tex]n=6*10*10=600[/tex]

adioabiola

The number of three-digit numbers that can be formed under each condition are as follows;

  • (a) 900

  • (a) 900(b) 648

  • (a) 900(b) 648(c) 180

  • (a) 900(b) 648(c) 180(d) 600

Provided there are no restrictions, there are 10 possible outcomes for each digit of a three-digit number.

For case (a): The leading digit cannot be zero

There are 9 options for the first digit and 10 for the remaining digits.

  • 9 × 10 × 10 = 900

For case (b): The leading digit cannot be zero and no repetition of digits is allowed.

In essence, the first digit has 9 outcomes, the second is supposed to be 10, but now has 9 since no repetition is allowed, while the 3rd digit now has 8.

  • 9 × 9 × 8 = 648

For case (c): The leading digit cannot be zero and the number must be a multiple of 5.

If a number is a multiple of five, it must end in 0 or 5

  • 9 × 10 × 2 = 180

For case (d): The number is at least 400.

Provided the number is at least 400, the first digit can only be 4, 5, 6, 7, 8 or 9. There are no restrictions for the remaining digits.

  • 6 × 10 × 10 = 600

Read more;

https://brainly.com/question/16176674