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

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BSchool Forum Moderator
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A palindrome is a number that reads the same forward and backward.  [#permalink]

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New post 31 Aug 2018, 10:58
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A palindrome is a number that reads the same forward and backward. For example - 1331.
How many 4-digit palindromes can be formed using two of the five digits - 1,3,5,7, and 9?

A. 10
B. 20
C. 30
D. 40
E. 60

Source: Experts Global

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

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New post 31 Aug 2018, 11:09
1
pushpitkc wrote:
A palindrome is a number that reads the same forward and backward. For example - 1331.
How many 4-digit palindromes can be formed using two of the five digits - 1,3,5,7, and 9?

A. 10
B. 20
C. 30
D. 40
E. 60

Source: Experts Global


How many 4-digit palindromes can be formed using two of the five digits - 1,3,5,7, and 9?

This means that the digits can not be repeated.

4 digit no looks like: _ _ _ _
We will start filling from the Thousands place.
Thousand's place can be filled in 5 ways.
Hundred's place can be filled in 4 ways.
Tenth's place has to be the same as hundreds place, so it can be filled in only 1 way.
One's Place has to be the same as hundreds place, so it can be filled in only 1 way.

Hence, 5x4x1x1= 20 ways.
My answer: B

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

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New post 01 Sep 2018, 00:08
1
pushpitkc wrote:
A palindrome is a number that reads the same forward and backward. For example - 1331.
How many 4-digit palindromes can be formed using two of the five digits - 1,3,5,7, and 9?

A. 10
B. 20
C. 30
D. 40
E. 60

Source: Experts Global


No of ways we can select the first of the four digits = 5
no of ways we can select the next = 4
no of ways we can select the penultimate digit = 1 ( should be same as the previous)
no of ways we can select the last digit = 1 ( should be same as the first)

= 5*4*1*1=20

another way probably to look at it would be

no of ways we can select 2 out of 5 = 5c2 =10
no of ways the selected 2 can be arranged in the required way = 2(we have 2 ways to place the first one , remaining 3 places are placed in 1 way)
=10*2=20
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A palindrome is a number that reads the same forward and backward.  [#permalink]

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New post 01 Sep 2018, 01:17
pushpitkc wrote:
A palindrome is a number that reads the same forward and backward. For example - 1331.
How many 4-digit palindromes can be formed using two of the five digits - 1,3,5,7, and 9?

A. 10
B. 20
C. 30
D. 40
E. 60

Source: Experts Global



( 13, 15, 17, 19) * 2 = 8

(35, 37,39)*2 = 6

(57,59)*2 = 4

(7,9) *2 = 2

8+6+4+2 = 20

What a relieve when you understand how to solve the problem !!!! :lol:
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Re: A palindrome is a number that reads the same forward and backward.  [#permalink]

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New post 01 Sep 2018, 03:57
if all four numbers are same such as 1111,5555

should we take this into accnt too
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Re: A palindrome is a number that reads the same forward and backward.  [#permalink]

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New post 01 Sep 2018, 04:01
sameeruce08 wrote:
if all four numbers are same such as 1111,5555

should we take this into accnt too


The question says 2 out of 5 , so we cannot take these into consideration.
Re: A palindrome is a number that reads the same forward and backward. &nbs [#permalink] 01 Sep 2018, 04:01
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