Answer:
Step-by-step explanation:
25C3 × 3! = 13800
Alternately,
25×24×23 = 13800
Permutation helps us to know the number of ways an object can be arranged in a particular manner. The number of ways in which the students can be selected for giving awards is 13,800.
Permutation helps us to know the number of ways an object can be arranged in a particular manner. A permutation is denoted by 'P'.
The combination helps us to know the number of ways an object can be arranged without a particular manner. A combination is denoted by 'C'.
[tex]^nC_r = \dfrac{n!}{(n-r)!r!}\ , \ \ ^nP_r = \dfrac{n!}{(n-r)!}[/tex]
where,
n is the number of choices available,
r is the choices to be made.
Given that in one year three awards (research, teaching, and service) will be given to a class of 25 graduate students in a specific department. Also, each student can receive at most one award.
The number of possible ways in which the students can be selected and the awards can be given is,
²⁵P₃ = 25!/(25-3)! = 25! / 22!
= (25 × 24 × 23 × 22!) / 22!
= 13,800
Hence, the number of ways in which the students can be selected for giving awards is 13,800.
Learn more about Permutation and Combination:
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