A WHITE GROUP MATHEMATICS SUPPLEMENTARY WEBSITE

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NTEZI RON

8:02 AM on October 1, 2014

i love and like this site for my teaching materials

Hi Shirley, you are most welcome. Wishing you a Happy Teacher's Day in advance. Best wishes for your family and god bless.

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Shirley

10:57 PM on August 24, 2014

Thank you so much for such valuable resource. You have saved me time to spend with my children...

From a grateful Mom/Teacher

From a grateful Mom/Teacher

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NTEZIYAREMYE RONALD

10:33 AM on May 27, 2014

i love teaching mathematics in all levels

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Ram Sah

8:03 PM on February 14, 2014

thank u very much for your great work i m grateful to u n salute you plz keep it up

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aimen

2:26 PM on December 8, 2013

I can't even believe i found this .. Pure treasure this is .. Thankyou soo much for this may god bless you and give you all the happiness of this world and the hereafter! Ei will be even more greatfull if you inlude summaries. And supplements for co ordinate geometry, discrete ramdom variable and quadratics.. tysm again

Hi Oliver, appreciate your encouraging comments. This site will be up and running as long as I am around. Peace.

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Oliver

10:01 AM on November 10, 2013

I found your notes very useful, please keep this site up for all the other students who need help. Thanks

Hi Ryan, thank you for your kind words.

Regarding your PnC question, I will get you started off:

Because the 5 blocks are distinctly labelled, despite them being placed in a circular fashion, permutation is conducted as if the blocks exist in a row format.

For (a), each of the five blocks can be painted a possible colour out of the available 4,

which means block A can be painted in 4 different ways, B can be painted in 4 different ways, ............. etc, ie this applies to the rest of the blocks. Hence total number of ways would simply be equal to (4)^5 =1024 ways (shown)

For (b), you may wish to consider the instances when both blocks A and B are painted with the same colour (try imagining them as a single unit to simplify matters), and subtract the possible number of ways this can happen from the answer you have in (a).

For (c), consider the total number of cases involved in situations where only 1, 2 or 3 colours are used in painting the blocks. (For example, when 1 colour is used for all 5 blocks, there are only 4 possible scenarios ). Once you have that, subtract this total from the answer in (a).

Hope this helps. Peace.

Regarding your PnC question, I will get you started off:

Because the 5 blocks are distinctly labelled, despite them being placed in a circular fashion, permutation is conducted as if the blocks exist in a row format.

For (a), each of the five blocks can be painted a possible colour out of the available 4,

which means block A can be painted in 4 different ways, B can be painted in 4 different ways, ............. etc, ie this applies to the rest of the blocks. Hence total number of ways would simply be equal to (4)^5 =1024 ways (shown)

For (b), you may wish to consider the instances when both blocks A and B are painted with the same colour (try imagining them as a single unit to simplify matters), and subtract the possible number of ways this can happen from the answer you have in (a).

For (c), consider the total number of cases involved in situations where only 1, 2 or 3 colours are used in painting the blocks. (For example, when 1 colour is used for all 5 blocks, there are only 4 possible scenarios ). Once you have that, subtract this total from the answer in (a).

Hope this helps. Peace.

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Ryan

2:25 AM on March 5, 2013

Hi i just happened to chance upon your site, and I think you have very good notes, which express clarity.

I happen to have a PnC questions, which I have been pondering over the last few days, but still can't seem to solve. (I am those kind that will keep thinking until I get an ans. So when I don't, it gets kinda frustrating ;( ) I really hope you can provide some insights.

Qn:

A developer has recently completed a condo project. There are five blocks A, B, C, D, E (they are arranged in a circle).

The developer has four colours available to paint the buildings. Each block can only be painted using a single colour. Find the number of ways to paint all the five blocks if

a) there are no restrictions

b) block A and B cannot be painted with the same colour

c) all four colours must be used.

I happen to have a PnC questions, which I have been pondering over the last few days, but still can't seem to solve. (I am those kind that will keep thinking until I get an ans. So when I don't, it gets kinda frustrating ;( ) I really hope you can provide some insights.

Qn:

A developer has recently completed a condo project. There are five blocks A, B, C, D, E (they are arranged in a circle).

The developer has four colours available to paint the buildings. Each block can only be painted using a single colour. Find the number of ways to paint all the five blocks if

a) there are no restrictions

b) block A and B cannot be painted with the same colour

c) all four colours must be used.

## Oops!

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