A boy went shopping with his father. He found a hat for $20 and he said to his father, "If you will lend me as much money as I have in my wallet, I will buy that hat." His father agreed and he bought the hat. Soon he saw a $20 shirt and he said to his father, "If you will lend me as much money as I now have in my wallet, I will buy that shirt." Again, his father agreed. They did it again with a $20 belt and the boy was now out of money. Let x represent the amount of money that the boy had at the beginning, a. Write an algebraic expression for the amount of money the boy had after buying the hat. b. How much money did his father lend the boy in order for him to buy the shirt? How much did he then have in total? c. Write an algebraic expression for the amount of money the boy have left after buying the shirt. d. Write an algebraic expression for the amount of money the boy had just before buying the belt. o. How much money did the boy have after buying the belt? f. How much money did the boy have at the beginning?
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.
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