In how many ways can a teacher arrange 6 students in the front row of a classroom with a total of 20 students?

Question

Ryan2 · Answer

This is a combination of 20 studants, 6 to 6: 
 C 2 , 6 ​ = ( 20 − 6 )! 6 ! 20 ! ​ = 14 ! 6 ! 20 ! ​ = 14 ! .6.5.4.3.2.1 20.19.18.17.16.15.14 ! ​ = 38 , 760 w a ys

Ryan2 · Answer

A teacher can arrange 6 students in the front row from a total of 20 students in 27,907,200 different ways. This is determined using the permutation formula, which accounts for the order in which the students are arranged. By applying the formula P(n, r) and simplifying, we arrive at the final count of arrangements. 
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In how many ways can a teacher arrange 6 students in the front row of a classroom with a total of 20 students?

Answer (2)

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