Question

The students in a class can be divided into groups of 5, 6, 7 and 8. What is the least number of student this class can have ?​

Answer 1

Answer:

ᴛʜᴇ ᴛᴏᴛᴀʟ ɴᴜᴍʙᴇʀ ᴏғ ᴡᴀʏs ᴛᴏ ғᴏʀᴍ ᴛʜʀᴇᴇ ᴛᴇᴀᴍs ɪs sᴀᴍᴇ ᴀs sᴇʟᴇᴄᴛɪɴɢ 4 sᴛᴜᴅᴇɴᴛs ᴏᴜᴛ ᴏғ 10 ᴛᴏ ғᴏʀᴍ ғɪʀsᴛ ᴛᴇᴀᴍ, ᴛʜᴇɴ 3 sᴛᴜᴅᴇɴᴛs ғʀᴏᴍ ʀᴇᴍᴀɪɴɪɴɢ 6 ᴛᴏ ғᴏʀᴍ sᴇᴄᴏɴᴅ ᴛᴇᴀᴍ ᴀɴᴅ ᴛʜᴇ ʀᴇᴍᴀɪɴɪɴɢ 3 ғᴏʀᴍs ᴀɴᴏᴛʜᴇʀ ᴛᴇᴀᴍ.

ᴛʜɪs ᴄᴀɴ ʙᴇ ᴅᴏɴᴇ ᴀs ғᴏʟʟᴏᴡs

= 3×(¹⁰C^4 ⁶C^3)/3!

=>10!6!/4!6!3!3!3! × 3

=> ¹⁰C^4 ⁵C^2 = 2100