91Ó°ÊÓ

How many four-digit numbers can be formed under each condition? (a) The leading digit cannot be zero. (b) The leading digit cannot be zero and no repetition of digits is allowed. (c) The leading digit cannot be zero and the number must be less than \( 5000 \). (d) The leading digit cannot be zero and the number must be even.

A combination lock will open when the right choice of three numbers (from \( 1 \) to \( 50 \), inclusive) is selected. How many different lock combinations are possible?

In how many orders can four girls and four boys walk through a doorway single file if (a) there are no restrictions? (b) the girls walk through before the boys?

In Exercises 9-32, write the first five terms of the sequence. (Assume that \( n \) begins with 1.) \( a_n = n (n - 1)(n - 2)\)

In Exercises 25 - 30, find the probability for the experiment of tossing a six-sided die twice. The sum is odd and no more than \( 7 \).

In Exercises 25 - 30, find the probability for the experiment of tossing a six-sided die twice. The sum is odd or prime

In Exercises 31 - 34, find the probability for the experiment of drawing two marbles (without replacement) from a bag containing one green, two yellow, and three red marbles. Both marbles are red.

In Exercises 31 - 34, find the probability for the experiment of drawing two marbles (without replacement) from a bag containing one green, two yellow, and three red marbles. Neither marble is yellow.

In Exercises 35 - 38, you are given the probability that an event will happen. Find the probability that the event will not happen. \( P(E) = 0.87 \)

From a pool of \( 12 \) candidates,the offices of president, vice-president, secretary, and treasurer will be filled. In how many different ways can the offices be filled?