Suppose that n balls are thrown independently and uniformly at random into n bins.
(a) find the conditional probability that bin i has one ball given that exactly one ball fell into the first three bins.
(b) find the conditional expectation of the number of balls in bin 1 under the condition that bin 2 received no balls.
(c) write an expression for the probability that bin 1 receives more balls than bin 2.

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Agroup of students want to create a garden. they do not know the exact measurements but they propose using a variable to represent the length and width of the garden. the length of the garden is 10 feet longer than double the width. use a single variable to write algebraic expressions for both the length and width of the garden. write an algebraic expression for the area of the garden. use mathematical terms to describe this expression.

Asequence is defined recursively using the formula f(n + 1) =f(n) - 5. which sequence could be