three girls a,b,c and five boys d,e,f,g,h are seated around a ciecular table.how many different arrangements are possible if no two girls are to sit together.Please show me how you got your answers.thanks,kerry
2006-08-08 01:59:33 · 8 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
it is 61443 exact
2006-08-08 03:09:08 · answer #1 · answered by Ariel 2 · 0⤊ 0⤋
The first question is easy, so I'll show you how to do the second one:
There are 8 seats arranged in a circle. You need to find the number of ineligible seating arrangements and subtract this from the total number of arrangements (which would be 8!).
So, if two girls sit together, we have:
3P2 * 8 * 6!
3P2 is the arrangement of 3 girls two at a time. Since there are 8 ways of doing this, we have 3P2*8. Now there are 6 people left (1 girl + 5 boys) who can be arranged in 6! ways. Therefore, we arrive at 3P2*8*6! = 3*8*720=17280
Now we can't have 3 girls sitting together either, so we do the same process above for 3 girls. i.e. 3P3*8*5! = 6*8*120 = 5760
So the total number of ineligible seating arrangements is: 17280+5760=23040
Subtracting this from the total number of arrangements (8!=40320), we have:
40320-23040 = 17280.
In conclusion, the total number of seating arrangements around a circular table without two girls sitting together is 17280.
2006-08-08 17:39:08 · answer #2 · answered by Anonymous · 0⤊ 0⤋
Hey, now, one question per question! :-D
Here's how you convert a number from decimal to some other base:
Divide the number by the new base. The remainder becomes the right-most digit of your answer. The quotient (the result of the division) becomes your "new number" -- you repeat the process, dividing it by the base number and marking down the remainder, etc.
So we start:
25,379 ÷ 8 = 3172, remainder *3*.
3172 ÷ 8 = 396, remainder *4*.
396 ÷ 8 = 49, remainder *4*.
49 ÷ 8 = 6, remainder *1*.
6 ÷ 8 = 0, remainder *6*.
So decimal 25,379 = 61443 in "octal."
Hope that helps!
2006-08-08 09:07:58 · answer #3 · answered by Jay H 5 · 0⤊ 0⤋
As an engineer, I like to show people the easy way to do things. Just open your windows calculator tool under accessories (or run "CALC") and click on scientific at the top under the VIEW drop menu. enter in your number then click on the oct base and it will convert it for you.
2006-08-08 09:15:57 · answer #4 · answered by Paco 211 2 · 0⤊ 0⤋
25379 to the base 8 is 61533 to the base 2.
2006-08-08 09:06:03 · answer #5 · answered by dimplesoft 3 · 0⤊ 0⤋
the base 8 number is 60003
2006-08-08 09:06:54 · answer #6 · answered by abhishek s 1 · 0⤊ 0⤋
ROTFLMSFAO!!!
'Paco 211' is certainly an engineer, 'Jay H' is a mathematician, and the others simply don't have a clue
Doug
2006-08-08 10:05:43 · answer #7 · answered by doug_donaghue 7 · 1⤊ 0⤋
why???why do you wanna know???what's it to you???
...ohhhkayyy...12???
2006-08-08 10:49:26 · answer #8 · answered by fred[because i can] 5 · 0⤊ 0⤋