Question

1.How many possible orderings of letters ABCDEFG are there?

2.How many strings of length 4 can be made using the letters ABCDEFG?

3.How many subsets of size 4 are there of the letters ABCDEFG.

4.How many possible strings are there of the letters "MATTER"?

5.Consider four books: an engineering book (E), a physics book (P), a history book (H), and an Art book (A).

Consider the following problem:

Suppose that the library has at least six copies of each of these books. In how many ways can we select six books?

Express this problem in terms of k-element selections on page 76 of the notes. What are the values of k and t?

6 .In rolling a fair die, what is the probability that a number less that 3 occurs?

7. Three microprocessors are randomly selected from a lot of 500 microprocessors among which 10 are defective. Find the probability of the event A of obtaining no defective microprocessors.

8. In an ordinary deck of 52 cards consisting of four suits, how many poker hands contain 4 cards of one denomination?

Really appreciate it if you could help me out ! Details needed.

Answer #1

1. (4 pts) Consider all bit strings of length six. a) How many
begin with 01? b) How many begin with 01 and end with 10? c) How
many begin with 01 or end with 10? d) How many have exactly three
1’s? 2. (8 pts) Suppose that a “word” is any string of six letters.
Repeated letters are allowed. For our purposes, vowels are the
letters a, e, i, o, and u. a) How many words are there? b)...

A standard 52-card poker deck consists of 4 suits and 13 ranks.
In how many ways can you draw 5 cards so that
1) there are no constraints?
2)all 5 cards are of same suits?
3) all four suits are present?
4) all cards are of distinct ranks?

how many strings of length 14 of lower case letters
from the English alphabet can be formed, if the first two letters
cannot Abe both vowels and the last letter must be a consonant?

1.) How many “words” are there of length 4, with distinct
letters, from the letters {a, b, c, d, e, f}, in which the letters
appear in increasing order alphabetically. A word is any ordering
of the six letters, not necessarily an English word.
2.) Prove that every graph has an even number of odd nodes.

How many possible 5-card poker hands are there that
have exactly 3 jacks? Reminder: card decks have 52 total cards.
There are 13 possible denominations of card (Ace, 2, 3, ..., 10,
jack, queen, king) and 4 possible suits (clubs, diamonds, hearts,
spades).

Consider the string of letters ”toomuchcringe”. How many
different strings/words can you form by re-arranging the above
letters, under the condition that n and g should be adjacent, AND
the string ”much” should stay together (and not be
re-arranged)?

How many “words” are there of length 4, with distinct letters,
from the letters {a, b, c, d, e, f}, in which the letters appear in
increasing order alphabetically. A word is any ordering of the six
letters, not necessarily an English word.

Determine how many different computer passwords are possible if
(a) the digits and letters can be repeated, and (b) if the digits
and letters cannot be repeated.
i. 4 digits followed by 2 letters
ii. 5 digits followed by 1 letter.
iii. 3 digits followed by 3 letters

How many different 4-letter radio station call letters can be
made
a. If the first letter must be K, Z, or P and no letter may be
repeated
b. if repeats are allowed (but the first letter is K, Z, or
P)?
c. How many of the 4-letter radio station call letters
(starting with K, Z, or P) have no repeats and end with the letter
J?

How
many different 4-letter radio station call letters can be made if
thr first letter must be K or W, repeats are allowed, but the call
letters cannot end in an O?

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