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A palindrome is a number that reads the same forward and backward. For

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Re: A palindrome is a number that reads the same forward and backward. For  [#permalink]

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New post 23 Jul 2019, 05:44
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We have 7 digits to fill in various possibilities using the digits 5,6 and 0.

No of possibilities for 1st digit = 2 (either 5 or 6. 0 is not a valid case as the number wouldn't be 7-digit then)
No of possibilities for 2nd digit = 3 (5,6 or 0)
No of possibilities for 3rd digit = 3 (5,6 or 0)
No of possibilities for 4th digit = 3 (5,6 or 0)
No of possibilities for 5th digit = 1 (same as 3rd digit)
No of possibilities for 6th digit = 1 (same as 2nd digit)
No of possibilities for 7th digit = 1 (same as 1st digit)

Hence, total no. of possibilities \(= 2*3*3*3*1*1*1 = 54\)

Option (B)
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A palindrome is a number that reads the same forward and backward. For  [#permalink]

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New post 23 Jul 2019, 06:02
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A palindrome is a number that reads the same forward and backward. For example, 3663 and 23232 are palindromes. If 7-digit palindromes are formed using one or more of the digits 5, 6 and 0, how many such palindromes are possible?


Here, the number has 7 digits and last 3 digits will depend on the first 3 digits. So effectively we have to arrange the first 4 digits only.

Things to keep in mind:
* The first digit cannot be '0', only '5' & '6' can take the first place.
* Remaining 3 places can be taken by any digit and repetition is allowed.

First place = 2 ways
Second place = 3 ways
Third place = 3 ways
Fourth place = 3 ways

Total different ways = 2*3*3*3 = 54
Total 54 different numbers are possible with given properties.

ANSWER : B
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Re: A palindrome is a number that reads the same forward and backward. For  [#permalink]

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New post 23 Jul 2019, 06:18
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There are 7 places and 3 numbers to choose from. But, since it is a palindrome, first 3 digits will be same as last 3 digits. Further, first digit can not be zero and the fourth digit can be any of the 3 numbers.
So, effectively we have 4 places to be filled from 3 numbers in the following way,
First Digit: 2 ways (either 5 or 6)
Second Digit: 3 ways (5,6 or 0)
Third Digit: 3 ways (5,6 or 0)
Fourth Digit: 3 ways (5,6 or 0)
Total number of possible ways: 2x3x3x3= 54 ways

Ans: B
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Re: A palindrome is a number that reads the same forward and backward. For  [#permalink]

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New post 23 Jul 2019, 07:56
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For 7 digit palindrome we need to find combinations for the first 4 digits. Last 3 digits will always need to be equal to first 3 digits, therefore cannot "control" them. Digit in the middle doesn't depend on any digits before or after. First digit has to be more than 0 therefore, 2 combinations of 5 or 6. 2nd, 3rth and 4th digits can be any of 3 digits (5,6,0):
Therefore, 2*3*3*3 = 54
Answer is B
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Re: A palindrome is a number that reads the same forward and backward. For  [#permalink]

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New post 23 Jul 2019, 08:43
Yes, correct 54.
I couldn't get through this question.
Easy after seeing explanations.
Thanks.
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Re: A palindrome is a number that reads the same forward and backward. For  [#permalink]

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New post 24 Jul 2019, 01:31
A 7-digit palindrome is formed when the 1st and 7th digit are the same,2nd and 6th are equal,3rd and 5th are equal and then 4th can be any number.
So, we will choose them in pairs. The first digit can be chosen in 2 ways,since 0 can not be chosen. Meaning you have just 1 option for the 7th digit.The 2nd digit you have 3 options meaning the 6th digit you have 1 option as well. 3rd digit can also be done in 3 ways and the 5th has to be the same number so you have 1 option as well. The 4th digit can be any number so you have 3 options there.hence,number of ways= 2*3*3*3*1*1*1
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Re: A palindrome is a number that reads the same forward and backward. For   [#permalink] 24 Jul 2019, 01:31

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