1.THERE ARE SIX PAIRS OF SHOES .IN HOW MANY WAYS WE CAN SELECT 8 SHOES SO THAT WE GET EXACTLY TWO PAIRS IN IT

2 THERE ARE 20 PEOPLE TO BE SEATED IN A ROW. TWO FRIENDS WANT TO SIT IN SUCH A WAY THAT NOT MORE THAN 8 PEOPLE BETWEEN THEM.HOW MANY WAYS IT IS POSSILE .

Hi,

For the first part, lets choose two pairs first so 8c2 and than we have 6 pairs left.
Now because we want TWO MORE SO 12C2 IS THA CASE OF CHOOSING choosing 2 shoes ouit of 6 leftover pairs but here 6 cases will be such in which both the shoes of same pair have been selected so its actuallty 12c2-6

Final answer is (12C2-6)8C2