d Combinations MCQ 1( A bag contains nine yellow balls )
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CoCmbinations MCQ 1( A bag contains nine yellow balls )

Combination MCQ 1: A bag contains nine yellow balls, three white balls and four red balls. In how many ways can two balls be drawn from the bag?

Solution:

 A bag contains nine yellow balls  …

Formula for combinations of n things with chosen  r at a time is

\[ _n\rm C_2= \frac {n!}{r!(n-r)!} \]

 

Here we have;

n = 9+3+4=16 (total balls)

\[ =\frac{16\times 15\times 14\times 13\times 12\times 11\times 10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 1}{2\times 1(14\times 13\times 12\times 11\times 10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1)} \]

r=2 ( two ball from among 16 balls to be chosen)

So, by above formula, the number of combinations in which we can take  two balls are;

\[ _16\rm C_2= \frac{16!}{2!(16-2)!} \]

We know;

16! = 16x15x14x13x12x11x10x9x8x7x6x5x4x3x1

2!=2×1

(16-2)!=14!=14x13x12x11x10x9x8x7x6x5x4x3x2x1

putting these values in above formula;

 

\[ = \frac{16 \times 15\times 14\times 13\times 12\times 11\times 10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 1}{2\times 1 (14\times 13\times 12\times 11\times 10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 1)} \]

 

common terms (as red color) in this fraction will cancel out — we then get;

\[ =\frac{16 \times 15}{2 \times 1}=120 \]

So, we can choose two balls from given in 120 different ways or schemes !

 

Information Corner

How to stay fit by avoiding obesity ?

This is a question which is very often asked on the internet and treatment to remove obesity is often asked and suggested frequently on health and fitness websites. Somewhere you will find suggested and practiced exercises and elsewhere a diet method or some medicine is given to give a finish to the damned obesity. But anyhow no recipe is fruitful to the maximum extent. This is because obesity though goes slowly away – thanks to the so called methodologies — but come back faster than earlier, and in this way healthy people frequently fed up of these in no time and then moves ahead to search for some new technique to reduce weight for all — but again in vain!

Finding Reason

Some people still succeed to find the genuine reason for there obesity or weight gaining. You know weight is gained not just because of excessive eating .But also due to the improper functioning of digestive organs. What happens if digestive system does not work properly? Answer is — ‘ perpetual constipation’! Constipation is a case when our liver or stomach is not able to fully digest fats in our food. And in this way the same is stored as an excess to our body mass giving a boost to weight of the body.This true even when one takes normal food but not in excess.
In short we can conclude that most people who complain that their perpetual constipation was inherited from their grand parents can overcome obesity if they succeed in removing the constipation problem along with taking routine meals.

We suggest you an innovative, magical, harmless and healthy way to get your obesity and constipation removed for all here. You can use this prescription as long as you wish without any fear!

Recipe for Preparation

Here is the simple recipe !

1- Take one quarter kg (250 gms) of cider honey

2- Take 50 gms of black  seeds. and smash.

3- Take 50 gms of Psyllium husk .

Just simply mix all these three ingredients in a jar. Use half of tea spoon with water before every meal you take. Wait not for result and carry on for consecutive 15 days at the least. You will feel the results automatically. All the ingredients are harmless and good for health for many unknown aspects as well.

If one uses this simple prescription consistently for long time , his tummy will be flattened and weight will be reduced. Hypertension and high blood pressure along with heart problems are also cureable.

Note: We are not doctors or medical consultants but are very sure that this works and there is no harm at all if used!

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