Question

in how many ways can a teacher create four teams of two students each out of 10 available students to compete against each other in a quiz competition​

Answer 1

Answer:

There are 10*9 = 90 different ways (assuming order matters). If order does not matter, then there are 90/2 = 45 different ways.

Answer 2

Answer:

Step-by-step explanation:

In this question , available students is 10 and 4 teams are forming with 2 students in each group .so we have to choose 8 students among 10

case:1- 10!/(10-8)!*8! =45 . but here also given that they are competing with each other in a quiz competition

case:2- ( 8!/6!*2!) (6!/4!*2!) (4!/2!*2!) *1/4! =105 ..............[all the groups are of equal size that's why we use 1/4!]

now from case 1 and case 2 = 45*105=4725

hence ,answer is 4725