MHB Combinatorics: Solve No Vowel Arrangement

Thread starter Roohul Amin
Start date Mar 24, 2017
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Combinatorics

Mar 24, 2017

Roohul Amin

please help solving this question
The letters of the word CONSTANTINOPLE are written on 14 cards, one on each card. The cards are shuffled and then arranged in a straight line: how many arrangements are there where no two vowels are next to each other?

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Mar 24, 2017

joypav

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Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...

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Thread 'Midpoint(s) of the unbounded number line'

Just chatting with my son about Maths and he casually mentioned that 0 would be the midpoint of the number line from -inf to +inf. I wondered whether it wouldn’t be more accurate to say there is no single midpoint. Couldn’t you make an argument that any real number is exactly halfway between -inf and +inf?

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Thread 'Arithmetic and our place value system'

A power has two parts. Base and Exponent. A number 423 in base 10 can be written in other bases as well: 1. 4* 10^2 + 2*10^1 + 3*10^0 = 423 2. 1*7^3 + 1*7^2 + 4*7^1 + 3*7^0 = 1143 3. 7*60^1 + 3*60^0 = 73 All three expressions are equal in quantity. But I have written the multiplier of powers to form numbers in different bases. Is this what place value system is in essence ?

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MHB Combinatorics: Solve No Vowel Arrangement

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Thread 'Trigonometry problem of interest'

Thread 'Midpoint(s) of the unbounded number line'

Thread 'Arithmetic and our place value system'

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