Question

P4: In the following problem, numbers do not begin with zero. (ex: 123456 is a 6-digit...

P4: In the following problem, numbers do not begin with zero. (ex: 123456 is a 6-digit number but 012345

is not.) You may leave your answers unsimplified.

(a)

How many 6-digit numbers are there?

(b)

How many 6-digit even numbers are there?

(c)

How many 6-digit numbers have all odd digits?

(d)

How many 6-digit numbers have all even digits?

(e)

How many 6-digit numbers have all distinct digits?

(f)

The numbers 3514153 and 8068608 are called

palindromic

because they read the same forwards and

backwards.

i.

How many 7-digit palindromic numbers are there?

ii.

How many 7-digit even palindromic numbers are there?

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

a) Number of 6 digit numbers = 9x105

= 900,000

b) Number of 6 digit even numbers = 9x104x5

= 450,000

c) Number of 6 digit numbers will all odd digits = 56

= 15,625

d) Number of 6 digit numbers will all even digits = 4 x 55 (first digit cannot be 0)

= 12,500

e) Number of 6 digit numbers with all distinct digits = 9 x 9P5

= 9 x 15120

= 136,080

f) In palindrome of 7 digits, the first 4 digits shall have choices and the last 3 will not have choice as it is same as the first 3 which is already selected

i. Number of seven digit palindromes = 9x10x10x10x1x1x1

= 9,000

ii. Number of seven digit even lindromic numbers = 4 x 10x10x10 x 1x1x1

= 4,000

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