The word CAMBRIDGE includes the three vowels A, E and I and six different consonants. i) Find the number of different arrangements using all nine letters. ii) How many of these arrangements start and end with a consonant, and do not have the three vowels together.

en the letters A, B, C, D, E, F, the number of 3 letter groups that can be made. B. Given 6 people in a club, the number of 6 person committees that are possible C. Given 6 people in a club, the number of ways that a president, secretary and treasurer L0Zd mu2 աալի Given 6 disting ds, the number of INIC. How many arrangements can be made using all the letters in the word OSOYOOS. A. 5040 B. 210 C. 2520 D. 105 the number of arrangements for theard TATTOO given that that the word be poppin. 2) The expression 321 x 320 x 319 x 318 can be simplified as nPr. The value of n + r =

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"?

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…

How many ways can you seat 8 people around a round table? Assume that the first person can choose any seat, and it doesn't matter where that person chooses. All that matters is where the others then choose to sit. Number different ways