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6 male students and 3 female students sit around a round table. The probability that no 2 female students sit beside each other can be expressed as a/b, where a and b are coprime positive integers. What is the value of a+b? Solution) For no female to sit beside each other the females should sit in alternate places.let the males also occupy alternate places then the no. of arrangements for male= (6-1)!=5! (circular permut.)the females can be give the 6 vacant places but there are only 3 female so arrangements= 6-P-3=20hence total no. of favourable outcomes= 20 . 5!and total outcomes= (9-1)!=8!hence P(e)= 20.5!/8!=20/8.7.6=5/84HENCE a+b=5+84=89(ANS)
For schedule consistency, you decide to require each officer to report for their eight-hour shift at 12 AM, 4 AM, 8 AM, 12 PM, 4 PM, or 8 PM. As the Director of Public Safety, you
Method of disks or the method of rings One of the simple methods for getting the cross-sectional area is to cut the object perpendicular to the axis of rotation. Carrying out
Find the discount factors -Linear interpolation: All rates should be calculated to 3 decimal places in % (e.g. 1.234%), the discount factors to 5 decimal places (e.g. 0.98765
how can we represent this mathematical equation on a graph y=2x-1
Question: Use Gauss elimination method to solve the following system of equations. -y +3z=4 2x-y-2z= 2 2x-2y+z =6 4x-y-7z= 0
Here, let's take a look at sums of the fundamental components and/or products of the fundamental components. To do this we'll require the following fact. Fact- Undetermined Co
Simplify following and write the answers with only positive exponents. (a) ( x 8.2 y -0.26 z 2 ) 0.5 (b) (x 3 y -4.1 / x -2.7 ) -3 Solution (a) (x 8.2
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Let Xn be a sequence of distinct real numbers. Defi ne E = {L : L is a subsequential limit of Xn}. Prove E is closed.
Mike sells on the average 15 newspapers per week (Monday – Friday). Find the probability that 2.1 In a given week he will sell all the newspapers
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