Respuesta :
Answer: 96
Step-by-step explanation:
A palindrome is a number that is the same when reading in both ways (right to left, and left to right), for example, 121
Then, we have 9 digits, and all the digits need to be even.
the options are: 0, 2, 4, 6, 8.
Now, we can think of a 9-digit number as 9 empty slots, and in each slot, we can put a number.
But because this is a palindrome, the first digit must be equal to the ninth, and the second digit must be equal to the eight, and so on.
So, we can think it as actually only 5 slots, where in each slot, we can put an even number, now let's count the options that we have in each selection.
For the first digit we have 4 options: 2, 4, 6 and 8 (0 is not counted here because if the first digit was a 0, then this would not be a 9-digit number).
for the second digit, we have also 4 options (because we already toked one, but now the 0 can be chosen)
for the third digit, we have 3 options
for the fourth digit, we have 2 options
for the fifth digit, we have only one option.
The total number of combinations is equal to the product of the number of options for each selection:
C = 4*4*3*2*1 = 96
