Lcm of 15 , 5 , and 9 ?

Mathematics

1 answer:

mihalych1998 [28]3 years ago

6 0

The answer is 45
Because 15x3=45,5x9 and 9x5=45 and 45 is the LCM

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There are 50 runners in a race. How many ways can the runners finish first, second, and third?

Dmitrij [34]

Number of ways can the runners finish first, second, and third is 1,17,600 .

<u>Step-by-step explanation:</u>

Permutation is the act of arranging the members of a set into a sequence or order, or, if the set is already ordered, rearranging (reordering) its elements—a process called permuting. For example, written as tuples, there are six permutations of the set {1,2,3}, namely: (1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), and (3,2,1). Formula of Permutation is : $P(n,r) = \frac{n!}{(n-r)!}$ where n is the number of things to choose from, and we choose r of them, no repetitions, order matters. Here , n = 50 , r= 3

⇒ $P(n,r) = \frac{n!}{(n-r)!}$

⇒ $P(50,3) = \frac{50!}{(50-3)!} = \frac{50(49)(48)47!}{47!}$

⇒ $P(50,3) = 50(49)(48)$

⇒ $P(50,3) = 1,17,600$

∴ Number of ways can the runners finish first, second, and third is 1,17,600 .

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