Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Calculate the number of ways two numbers can be chosen from the set <img alt="\{1,4,7,10, \ldots, 142,145,148\}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5C%7B1%2C4%2C7%2C10%2C%20%5Cld

Calculate the number of ways two numbers can be chosen from the set \{1,4,7,10, \ldots, 142,145,148\} and multiplied together to obtain a product that is a multiple of 5 but not a multiple of 3 or 7.

 

Option: 1

2806


Option: 2

 5208


Option: 3

4408


Option: 4

 1280


Answers (1)

best_answer

To calculate the number of ways two numbers can be chosen from the set \{1,4,7,10, \ldots, 142,145,148\} and multiplied together to obtain a product that is a multiple of 5 but not a multiple of 3 or 7 , we need to consider the factors of 5,3 , and 7 .

First, let's analyze the given set: \{1,4,7,10, \ldots, 142,145,148\}
Numbers divisible by 5: 5,10,15, \ldots, 145
Numbers divisible by 3: 3,6,9, \ldots, 147
Numbers divisible by 7: 7,14,21, \ldots, 147

To find the number of ways to choose two numbers such that their product is a multiple of 5 but not a multiple of 3 or 7 , we can break it down into cases:

Case 1: Both numbers are divisible by 5
There are 29 numbers divisible by 5 in the given set. Therefore, the number of ways to choose two numbers divisible by 5 is ( 29 choose 2)= 406 ways.

Case 2: One number is divisible by 5 and the other is not divisible by 3 or 7
There are (29 \times 116)=3364 ways to choose one number divisible by 5 and one number not divisible by 3 or 7 .

Case 3: One number is divisible by 5 and the other is divisible by 3 or 7
There are (29 \times 22)=638 ways to choose one number divisible by 5 and one number divisible by 3 or 7.

Therefore, the total number of ways to choose two numbers from the set \{1,4,7,10, \ldots, 142,145,148\}and multiplied together to obtain a product that is a multiple of 5 but not a multiple of 3 or 7 is 406+3364+638=4408 ways.

Thus, there are 4408 ways to choose two numbers from the given set such that their product is a multiple of 5 but not a multiple of 3 or 7.

Posted by

Divya Prakash Singh

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2026: JCECEB invites fresh applications for Jharkhand state merit list correction

Latest Question