How many different 5​-letter words can be made:   a.  if the first letter must be C, Y, or T and no letter may be​ repeated?   b.  if repeats are allowed​ (but the first letter is C, Y, or T​)?   c.  How many of the 5​-letter words​ (starting with C, Y, or T​) with no repeats end in S​?

A class has 32 students. In how many different ways can six students form a group for an activity? (Assume the order of the students is not important.) There are different ways that the six students can form a group for an activity. (Type a whole number.)

Given the 8 letters in the word ABSOLUTE, a. How many ways can the letters be rearranged? b. How many arrangements can be formed if A and B must be together? c. How many arrangements can be formed if the word must start with a vowel (A, E, O, or U) and end with "A" or "T"?

At a music​ festival, there are seven bands scheduled to​ play, numbered 1 through 7. a. How many different ways can these bands be arranged to​ perform? b. If band 2 is performing first and band 5 ​last, then how many ways can their appearances be​ scheduled?

5 different elves (Sue, Marcia, Cher, Jane, and Johnny) each make a different toy (ball, car, top, sled, or train). Each elf wears a different color (green, yellow, blue, red, or orange) and each builds a different number of toys. Use the poem below to decipher which elf wore what color and made how many of what toy!! ---------------------------------------------------- The Boss's pack held thirty toys Made by his elfin crew; And though none made the same amount, Each elf made more than two. The elf named Cher made one more toy Than the elf who dressed in reds, But Cher made one less holiday toy Than the elf who made the sleds. Spry Johnny elf made racing cars; Five toys were made by Jane. The elf who dressed in yellow suits Made each and every train. The elf who always dressed in green Made one-third as many as Sue. Cute Marcia elf was dressed in orange, And one elf dressed in blue. The elf who made the spinning tops Made the most toys of them all. Another perky, smiling elf Made each…

Twelve wedding guests are assigned seats in the northwest corner of the reception hall. Show all work. a. If the seats are numbered, how many ways can the 12 guests be seated in 3 chairs? b. If the reception hall instead assigned 6 guests per table, how many ways can 12 guests be assigned to a table?

How many three – digit numbers can be formed fromthe digits 1, 2, 5, 6, and 9 if each digit can be usedonly once? 6.1 From the answer above, in how many area. even? b. Odd? c. Numbers greater than 600? d. How many three digit numbers can be formedif repetition is allowed?

Bread Meat Spread Mayo (0.5) Honey Oat Ham (0.4) (0.6) Mustard Turkey (0.4) White (0.2) (0.6) Ranch (0.3)

There are 125 students in a class. At least how many students came from the same state if there are 16 states in the country? O 7 O 8 O 10