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How many integers between 500 and 1000 contain both the digits 3 and 4?

 Jun 10, 2021
 #1
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According to the question, 

All the integers between 500 & 1000 are 3 digit no.s greater than 500. 

 

∴ First place may have digits 5,6,7,8 & 9 = 5 possibilities

Second & third place may have digits 3 or 4 = 2 possibilities 

 

⇒Total no. of possibilities \(=5*2\)

                                         \(=10\)

 

Thus, total no. of such integers are 10. 

 

 

~Amy 

 Jun 10, 2021
 #2
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How many integers between 500 and 1000 contain both the digits 3 and 4?   

 

Two ways the integer can contain both 3 and 4 ... to wit, it ends with 34 or 43. 

 

So, in the 500's there are 534 and 543  

similarly there are             634 and 643 

                                         734 and 743  

                                         834 and 843  

                                         934 and 943              total:  10 such integers   

.

 Jun 10, 2021

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