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2 years ago

S = {1, 2, …, 100}. How many permutations are there of S in which the number 1 is next to at least one even number?

Mathematics

1 answer:

e-lub [12.9K]2 years ago

6 0

Answer:

Check the explanation

Step-by-step explanation:

in this particular type of problems,we have to go with the cases.we know there would be a 50 odd-even pairs between 1 and 100.

1st case: 1 is placed at the head position of given set S.so there is a chance of only one even number beside 1.so there are 50×98!

2nd case: 1 is placed at tail position of S.so there is again a chance of one even number beside 1. so there are

50×98!

3rd case: 1 is placed neither at head nor at tail.1 can be at rest 98 places.lets fix the place of 1.then the choices are difference between permuting all the numbers and 1 surrounded by two odd numbers.

i.e., 99! - 49p2 ×97!

so total choces are = 2×50×98! + 99! - 49p2 × 97!

= 7448 × 97! + 99!

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2 years ago

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Answer:

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Step-by-step explanation:

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2 years ago

An arena receives $1,700 per event for 12 concerts. If the costs for this sponsorship total $14,000, what is the profit margin f

miss Akunina [59]

Answer:

total profit margin for all 12 concert is $6,400.

profit margin for all one concert is $533.33

Step-by-step explanation:

Amount of money received for one event = $1700

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Total money received for 12 event = $1700 *12 = $20,400

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Total money earned is $20,400

Therefore profit margin = money earned - total investment

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Therefore total profit margin for all 12 concert is $6,400.

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2 years ago

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Paraphin [41]

Answer:

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Distributive Property states that when a number is multiplied by the sum of two numbers, the first number can be distributed to both of those numbers and multiplied by each of them separately.

If $a\cdot(b+c) =a\cdot b + a\cdot c$