Question

How many palindromes are there between 4000 and 83000

Answer 1

$\huge{Answer}$

>>>790 palindromes are there.

$\huge{Divya}$❤

Answer 2

Answer:

There are 790 palindromes between 4000 and 83000

Explanation:

Since, 4000 < N < 83000, we have to consider various cases for 4-digit numbers and 5-digit numbers

Case 1:    for  4-digit numbers

1st digit can be from 4–9 (6 choices)

2nd digit can be from 0–9 (10 choices)

3rd digit must be same as 2nd digit (1 choice)

4th digit must be same as 1st digit (1 choice)

Total 4-digit palindrome numbers > 4000 =6×10×1×1=60

Case 2: 5-digit numbers < 8000  

1st digit can be from 1–7 (7 choices)

2nd digit can be from 0–9 (10 choices)

3rd digit can be from 0–9 (10 choices)

4th digit must be same as 2nd digit (1 choice)

5th digit must be same as 1st digit (1 choice)

Total 5-digit palindrome numbers < 80000 =7×10×10×1×1=700

Case 3: 5-digit numbers > 80000 and < 83000

1st digit can be only 8 (1 choice)

2nd digit can be from 0–2 (3 choices)

3rd digit can be from 0–9 (10 choices)

4th digit must be same as 2nd digit (1 choice)

5th digit must be same as 1st digit (1 choice)

Total 5-digit palindrome numbers > 80000 and < 83000 =1×30×10×1×1=30

Total Palindrome numbers N, such that 4000 < N < 83000

=60+700+30

=790