I need the answer in 2 hours!!!!!!!!!!! Consider all bit strings of length 10. a
ID: 3807568 • Letter: I
Question
I need the answer in 2 hours!!!!!!!!!!!
Consider all bit strings of length 10. a) How many begin with 101? b) How many begin with 10 and end with 11? c) How many begin with 10 or end with 11? d) How many have exactly three 1's? 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) How many words begin with A or B? c) How many words begin with a vowel and end with a vowel? d) How many words have no vowels? e) How many words have exactly one vowel? A professor teaching a Discrete Math course gives a multiple choice quiz that has five questions, each with four possible responses: a, b, c, d. What is the minimum number of students that must be in the professor's class in order to guarantee that at least three answer sheets must be identical? (Assume that no answers are left blank.) You pick cards one at a time without replacement from an ordinary deck of 52 playing cards. What is the minimum number of cards you must pick in order to guarantee that you get a) a pair (for example, two kings or two 5s) b) three of a kind (for example, three 7s) Use the binomial theorem to expand (x + y)^5.Explanation / Answer
4) a) n = 13.1 + 1 = 14
b) n = 13.2 + 1 = 27
5) ( x+y ) 5 = 5C0 (x)5 (y)0 + 5C1 (x)4 (y)1 + 5C2 (x)3 (y)2 + 5C3 (x)2 (y)3 + 5C4 (x)1 (y)4 + 5C5 (x)0 (y)5
= x5 + 5x4 y + 10x3 y2 + 10x2 y3 + 5 x y4 + y5
3) this is pigeonhole problem in this question each student should do 5 questions and for which there are 4 possible responses for each question therefore
the total no of boxes i.e k = 45
therefore inorder to ensure that at least one box has atleast 3 students in it , the minimum students are i.e
N = ( R - 1 ) .K + 1
= ( 3 - 1 ) . 45 + 1
= ( 2 ) . 256 + 1
= 512 + 1
= 513 minimum no of students
2) a) 26 letters = the no of words = 266
b) the words begin with A or B is 2 * 265
c) the words begin with vowel and end with vowel is 25 * 264
d) the words which does not have vowels is 216
e) the words that have exactly one vowel is 6 * 5 * 215 i.e 30 * 215 = 960
1) a) the no of bit strings that begin with 101 is 27 = 128
b) the no of bit strings begin with 10 and end with 11 is 26 = 64
c) the no of bit strings starts with 10 is 28 and the no of bit strings end with 11 is 28
therefore the no of bitstrings start with 10 and end with 11 is 26
= 28 + 28 + 26
= 26( 22 + 22 + 1 )
= 9 * 26
= 576
d) the no of bit strings that have exactly three 1's is 10C3 i.e
= 10C3
= 10 ! / ( 10 - 3 ) ! * 3!
= 120