theorems

Parin Sir > theorems
05
Jun
Examples

(1) Evaluate  : \frac{20!}{17!}

Soln. We have,  \frac{20!}{17!... </p> <div class=

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05
Jun
Combination

☼ COMBINATION  :   When  we have to choose a certain number of  objects from a given set of  objects in such a way that the order of  selection is not important, the selection is known as a combination. Consider the following example…

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04
Jun
Circular Permutation

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☼ Circular Permutation  :   The total number of  circular permutations of  n distinct objects taken all at a time   = 

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04
Jun
Permutations

☼ PERMUTATIONS  :   In  the above example, 2 objects were selected from 3 objects in such a way that the order of  the arrangements is important.

Now, if there were  n = 10 objects and  r  = 3 objects were to be selected, then we …

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04
Jun
Definition of  Fundamental principal of  counting

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☼ Definition of  Fundamental principal of  counting  :   If one operation can be performed in m ways and if corresponding to each of  the m…

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04
Jun
Permutation And Combination

☼ Factorials  :   Permutation and Combination is a topic which requires use of  the concept of  factorials. A factorial is the number obtained by multiplying all the positive integers less than or equal to a given positive integer. T…

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04
Jun
Examples

(1) In what proportion must rice at Rs. 12.50 per kg. be mixed with rice at Rs. 15.20 per kg., so that the mixture be worth Rs. 14.00 per kg. ?

Solution.

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03
Jun
ALLIGATION OR MIXTURE

☼ Alligations  is the rule that helps us to find the amount in which two different quantities of  a substance are mixed so as to arrive at average cost.

☼ If  the gradients are mixed in some ratio,   then

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03
Jun
Examples(2)

(8) If  a, b, c, d  are four consecutive odd integers, then give its average in the form of  a.

Soln.    A          b          c

Here, a, b, c, d are in A.P.

\th... </p> <div class=

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03
Jun
Examples

Examples  :

(1) Find the average of  first  7 prime numbers.

Soln. Required average  = 

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