a palindrome is a number like 252, which reads the same forward and backward if the digits 1,1,1,2 and 2 are randomly ordered to form a five digit integer what is the probability the resulting integer is a palindrome express your answer as a common fraction

The probability that the resulting integer is a palindrome is 1/5, or 0.2 expressed as a decimal.

The five-digit number must take the form of XY2YX in order for the given digits (1,1,1,1,2,2) to create a palindrome.

There are two instances to think about:
1) X=1 and Y=1:

In this case, the integer will be 21112.
2) X=1 and Y=2:

In this case, the integer will be 12121.
There are a total of 5! (5 factorial) ways to arrange the digits (1,1,1,2,2).

To calculate the total number of ways to arrange the digits 1, 1, 1, 2, and 2, we can use the formula for permutations with repetition:

n! / (r1! * r2! * ... * rk!)
Total arrangements = 5! / (3! * 2!) = 120 / (6 * 2) = 10
Only 2 of these 10 potential combinations result in palindromes.

There are precisely 2 options for B (specifically, 0 and 5) that make the number ABB divisible by 5 out of the total of 10 options for A and 10 options for B.

As a result, there are two possibilities for the digits ABB to divide the total number by 5.

This means that there are a total of 50 six-digit palindromes of the type 5ABBA5 that are divisible by 55.

As a result, the likelihood of a palindrome is:
Probability = (Number of palindromes) / (Total arrangements)

P(palindrome) = 2 / 10

P(palindrome) = 1/5

There are only two palindromes that can be formed using the digits 1, 1, 1, 2, and 2. They are 12121 and 21112.

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