The combination helps us to know the number of ways an object can be arranged without a particular manner. The number of different groups of 5 shirts can Omar can take is 126.
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!}[/tex]
where,
n is the number of choices available,
r is the choices to be made.
Given that Omar is packing his bags for his vacation. he has 9 unique shirts but only 5 can fit in his bag. Therefore, the given information is,
Number of Choices = 9
Number of choices that can be selected = 5
Now, the number of different groups of 5 shirts can Omar can take is,
Number of groups = ⁹C₅
= 9!/ [5! (9-5)!]
= 9! / (5! × 4!)
= 362,880 / (120 × 24)
= 126
Hence, the number of different groups of 5 shirts can Omar can take is 126.
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