There are students in a small class. To make a team, the names of some of them will be drawn from a hat. How many different teams of students are possible?
Answer (2)
e . g a s ma ll c l a ss ha s 15 s t u d e n t s an d w e w i ll c h oose 3 − p erso n t e am t h e n u mb er o f p oss ib l e t e am s i s ( k n ) = ( 3 15 ) = 3 ! ⋅ ( 15 − 3 )! 15 ! = 2 ⋅ 3 ⋅ 12 ! 12 ! ⋅ 13 ⋅ 14 ⋅ 15 = 2 ⋅ 3 13 ⋅ 2 ⋅ 7 ⋅ 3 ⋅ 5 = 13 ⋅ 7 ⋅ 5 = 455
To find the number of different teams of students from a class, use the combinations formula ( k n ) = k ! ⋅ ( n − k )! n ! . For example, from a class of 10 students, the number of ways to choose a team of 3 is 120. This formula helps calculate how many unique groups can be formed without regard to order.
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