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Probability is the number of chances in which a particular is likely to occur.
Example : 1 There are 3 blue balls and 5 red balls is a box. A student is asked to pick a ball out of the box. What is the probability for the ball to be a red ball? The number of blue balls = 3 The number of red balls = 4 The total number of balls = 3 + 4 = 7 The probability for the picked-ball to be a red ball is = = (the number of red balls in the box / the total number of balls in the box) = 4/7 SO, the probability for the ball to be a red ball = 4/7 Answer : 4/7 Combinations : Combination is the way in which a particular design can be arranged. Example : 2 There are 4 varieties of ice-cream in a parlour. Each variety comes in 5 colours. In total, the ice-cream is coming in how many combinations? The number of varieties of ice-cream = 4 The number of colours in each variety = 5 The number of combinations in which the ice-cream comes = 4 x 5 = 20 Answer : 20 Permutations : A Permutation is a combination but in an orderly manner. Example : 3 There are five singers waiting to sing in a competition one by one. In how many permutations in which they can sing? The permutations in which they can sing = 5 x 4 x 3 x 2 x 1 = 20 x 6 = 120 The number of ways in which the five singers can sing in the competition = 120 NOTE : (5 x 4 x 3 x 2 x 1) This is called 5 factorial. 5 factorial can be written as 5! 5! = 5 x 4 x 3 x 2 x 1 8! = 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
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