91Ó°ÊÓ

Find the number of distinguishable permutations of the group of letters. \(\mathbf{A}, \mathbf{L}, \mathbf{G}, \mathbf{E}, \mathbf{B}, \mathbf{R}, \mathbf{A}\)

You draw one card at random from a standard deck of 52 playing cards. Find the probability that (a) the card is an even-numbered card, (b) the card is a heart or a diamond, and (c) the card is a nine or a face card.

Find the sum using the formulas for the sums of powers of integers. $$\sum_{n=1}^{15} n$$

A shipment of 12 microwave ovens contains three defective units. A vending company has ordered four units, and because each has identical packaging, the selection will be random. What is the probability that (a) all four units are good, (b) exactly two units are good, and (c) at least two units are good?

Find the sum of the finite arithmetic sequence. $$2+4+6+8+10+12+14+16+18+20$$

ATM personal identification number (PIN) codes typically consist of four-digit sequences of numbers. Find the probability that if you forget your PIN, then you can guess the correct sequence (a) at random and (b) when you recall the first two digits.

Random Number Generator A random number generator on a computer selects two integers from 1 through \(40 .\) What is the probability that (a) both numbers are even, (b) one number is even and one number is odd, (c) both numbers are less than \(30,\) and (d) the same number is selected twice?

Write the first five terms of the sequence defined recursively. $$a_{1}=28, \quad a_{k+1}=a_{k}-4$$

Evaluate \(_{n} C_{r}\) using the formula from this section. \(_{4} C_{1}\)

Finding the Probability of a Complement You are given the probability that an event will happen. Find the probability that the event will not happen. $$P(E)=0.87$$