A box contains three white balls, four black balls and three red balls. Find the number of ways in which three balls can be drawn from the box so that, a) At least one of the balls is black. b) With no restriction c) One ball of each colors.
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
Question #07
i) A box contains three white balls, four black balls and three red balls. Find the number of ways in which three balls can be drawn from the box so that,
a) At least one of the balls is black.
b) With no restriction
c) One ball of each colors.
ii) Using the digits 1, 2, 3 and 5, how many 4 digit numbers can be formed if
a) The first digit must be 1 and repetition of the digits is allowed?
b) The first digit must be 1 and repetition of the digits is not allowed?
c) The number must be divisible by 2 and repetion is allowed?
b) The number must be divisible by 2 and repetion is not allowed?
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