How many arrangements of the letters of GRACIOUS are there with the vowels occur consecutively (like GRCAOIUS, not GACRIOUS)? (Letters do not need to be in alphabetical order)
How many arrangements of the letters of GRACIOUS are there with the vowels occur consecutively (like GRCAOIUS, not GACRIOUS)? (Letters do not need to be in alphabetical order)
Simple Problems: Please express your answer in the form of (i) P(n,k) or (ii) [k] [n] or (iii) some other product for some n and k. a. The Russian alphabet...
Suppose a subset of 8 different days of the year is selected at random. What is the probability that each day is from a different month? (For simplicity, assume a year has 12 months and 30...
Assume that 12 students, including John, are working on the project report, which contains an introduction, 4 chapters, and a conclusion for a total of 6 sections. (1) In how many ways can the...
For this problem, assume that 2, 6, 5, and 4 are equally likely, a 1 is three times as likely as a 4, and a 3 is four times as likely as a 1. (1) What is the value of w2? (2)...
In this version, you are to form a 4-digit number from the digits 1, 2, 3, 4, 7, 8, and 9, using each at most once. How many of these are less than 5000?
involving the sum of two die rolls. (1) What is the probability they sum to 9, 3, or 6? (2) What is the probability they sum to at least 7?
1. For this problem, assume the cooler contains 32 cans, 22 of which are regular, and the rest of which are diet. What is the probability of selecting 5 cans from the cooler so that at least 4...
For this problem, assume that you are to pick 4 cars from the motor pool, which contains 7 subcompact cars, 6 compact cars, and 4 midsize cars. How many ways can you pick the cars so...
For this problem, assume that 2, 6, 5, and 4 are equally likely, a 1 is three times as likely as a 4, and a 3 is four times as likely as a 1. (1) What is the value of w2? (2) What is...
Assume that there are 15 frozen dinners: 6 pasta, 5 chicken, and 4 seafood dinners. The student selects 5 of them. What is the probability that at least 2 of the dinners selected are pasta dinners...
For this problem, assume that you are to pick 4 cars from the motor pool, which contains 7 subcompact cars, 6 compact cars, and 4 midsize cars. How many ways can you pick the cars so not all are...
Assume that there are 9 girls and 8 boys in the neighborhood club, and a team of 5 is to be selected. (1) How many different teams can be selected? (2) How many different teams can be...
student who wants to buy 3 CDs, but assume that there are 3 CDs featuring the piano, 4 CDs featuring the trumpet, and 5 CDs featuring the saxophone. (1) In how many different ways can...
A computer password can use all digits (0-9) and all letters (a-z) that are case sensitive (upper and lower). How many different permutations of 5-figure passwords are there if there is no repeated...
how many permutations can be formed by the letters of the word 'VOWELS' when 1>the letters can be placed anywhere 2>each word begins with E 3>each word begins with O and ends...
Assume that there are 5 unfilled roles: 3 male and 2 female. There are 6 men and 6 women, including Ann, auditioning for a part in the play. How many of these casts include Ann?
In how many ways can the letters of the word INDIVIDUAL be arranged
How many positive 10-digit integers are there with the property that for each digit N, the number of adjacent N's is at most N?
Suppose that a department contains 8 men and 16 women. How many ways are there to form a committee with 6 members if it must have strictly more women than men?