a) How many 3-digit numbers are there? b) How many 3-digit numbers can you make with...

a) How many 3-digit numbers are there?

b) How many 3-digit numbers can you make with all three digits different?

c) How many of the numbers is part b) are odd?

Solutions

Expert Solution

a) Each of the three digits have 10 different choices except for the leading digit which cannot be 0. Therefore, the number of 3 digit numbers

= 9 * 10 * 10 = 900.

b) The first digit has 9 choices as explained already. Since one digit is used up, the second digit has 9 choices and so the third digit has 8 choices.

In all the number of such 3 digit numbers

= 9 * 9 * 8

= 648.

c) If the last digit is odd the number is odd. Thus we have 5 choices for the last digit.

The first digit has 8 choices as 0 is forbidden in addition to the already chosen last digit.

The second digit has 8 choices left.

Number of such odd numbers = 5 * 8 * 8 = 320.

orchestra answered 1 year ago

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