I would like to know how to calculate the amount of numbers between 1000 and 100000 that do not cont

glitinosim3

glitinosim3

Answered question

2022-07-13

I would like to know how to calculate the amount of numbers between 1000 and 100000 that do not contain 2,7 or 8. I had this question in my exam today and, since I have never been able to do probability and combinatorics properly, it's very likely I got it wrong. Could you please show me how to calculate it?
What I thought was: for 4 digit integers, calculate the total amount of possible numbers. Then calculate all numbers which do not contain 2,7 or 8 and deduce that from the total amount of 4 digit numbers. Repeat process for 5 digit integers and sum them up.

Answer & Explanation

Ronald Hickman

Ronald Hickman

Beginner2022-07-14Added 18 answers

Hint: writing decimal numbers between 1000 10 and 100000 10 which do not contain the 3 given digits is equivalent to writing the numbers in base 10-3=7 between 1000 7 and 100000 7
Gauge Terrell

Gauge Terrell

Beginner2022-07-15Added 5 answers

- Label digits from left to right A,B,C,D,E,F.
- First, count only 5-digit numbers (B to F), then add 1 to the count for 100000.
- For each digit there are 7 numbers to choose from.
- BC cannot be 00 for a 5-digit number.
Number of integers from 1000 to 100000 (inclusive) without any digit being 2,7,8 is given by:
1 100000 + ( 7 B × 7 C 1 B C = 00 ) ( 7 D × 7 E × 7 F ) = 16465

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