Posts Tagged ‘permutations’

The Bookstore Shelf

Saturday, December 15th, 2018

Harry was busy arranging books on a book shelf at the Wide Horizons Book Shop. Harry was positioning two copies of Inferno,  three copies of The Da Vinci Code and four of Origin.

A little boy stood there watching Harry.

“I’ll bet you don’t know in how many ways you can arrange those books on the shelf,” said Lenny teasingly.

Harry looked behind him and saw the grinning, mischievous face of a five-year old looking up at him.

“Well, obviously in just six ways, kid,” said Harry.

“Not if you mix all the books in all possible ways,” replied Lenny impishly.

“What a pesky kid,” said Harry backing off to stand away from the book shelf and scratch his head.

“Just to give you a hand, mister, check how many different words you can make with the letter group ‘mississim’ and you’ll have the answer. That way you won’t have to move the books around,” said Lenny on his way out of the store.

In how many different ways would you say the books can be arranged?

Six Colored Balls

Wednesday, November 14th, 2018

“Daddy, what are these six colored balls for?”

“Well, son, you’ll notice that three of them are red, two blue and one is green. The red balls all have the number one printed on them, the blue balls all have the number two printed on them, and the green one the number three printed on it,” said daddy, holding up the balls.

“They have very pretty colors, daddy,” said Lenny, “so what do you have in mind.”

“Let’s see how many different six-digit numbers you can make, son,” replied daddy.

“I know already, daddy,” smiled Lenny, “but for the chemistry set you promised me, I’ll tell you how many numbers with digits from one to five can be made with these balls,” said Lenny enthusiastically.

“That’s certainly a deal, son,” said a nonplussed daddy.

How many distinct six figure numbers do you say can be made using these balls?

And, how many distinct numbers with one to five digits can be made with these balls?

The Date Lineup

Wednesday, July 25th, 2018

Wilbur went to a dating club one Saturday evening to pick up a date for dinner.

As he entered The Quick Date Club, he saw what he wanted: a tall brunette with a shapely figure. She had the name Alice displayed on a badge dangling from a well-filled blouse.

The system at the The Quick Date Club was to seat an equal number of men and women at random in a row with eight numbered chairs, the numbers and names to be displayed on a screen on the wall.

The rule was that any female sitting next to a male would be eligible for a date request, unmatched persons to be recycled for the next round.

What would you say was the probability that Wilbur sat next to Alice so he could invite her for dinner?

At Chez Clouseau’s

Saturday, June 25th, 2016

On a winter’s evening, two couples, Jack and Jill, Willy and Lola, went to the famous French restaurant Chez Clouseau in New York to delight their taste buds with a three star Michelin cuisine.

After entering the plush lobby, they had to check their coats in the wardrobe, which was attended by Molly, a distrait blonde.

“Welcome to Chez Clouseau, y’all. Please check in your coats, y’all” said Molly, gracefully extending her arm, fingers glittering with rings.

The couples obliged and were handed four numbered plastic cards engraved with the Chez Clouseau logo, an inscripton with two crossed red wine bottles on a fleur-de-lis background, upon which they were led at a brisk but elegant pace by the maitre d’ to their table.

After dining at a tastefully set table with dishes crisscrossed in an artistically random fashion with sprayed-on green stripes – just missing some small stacks of colorful tidbits – drinking expensive vintage Bordeaux wine, and then paying the exorbitant bill, the couples returned in a financially decimated and bewildered state to the wardrobe to at least recover their coats.

“Our coats please,” commanded Jack, handing the plastic cards to Molly so she could connect the right owner with the right coat.

“Thank you mister,” beamed Molly with a charming smile. Just then a handsome French waiter passed by with a tray holding several full wine glasses, and Molly’s eyes glued onto and followed the garçon, dropping the plastic cards, which fell helter-skelter in a random fashion on the floor behind the wardrobe counter.

“Oops,” she blushed all flustered, “Really, how could this all have happened, y’all.”

She quickly checked the numbers on the plastic cards and handed Jack and Jill and Herman and Lola the coats corresponding to the numbers on the cards and the coat rack.

As the ordered taxi was beeping loudly outside, the two couples grabbed the coats given to them and raced out the door in a rush to leave. Molly didn’t get a tip.

What is the probability that at least one of the four received their own coat on checking this in the taxi? And the probability that one of the couples both received their own coat? That both couples received their respective own coats?


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