Advertisements
Advertisements
प्रश्न
How many ways can the product a2 b3 c4 be expressed without exponents?
उत्तर
The given term is a2b3c4
The factors are a, b, c
Number of a’s = 2
Number of b’s = 3
Number of c’s = 4
a2b3c4 = a × a × b × b × b × c × c × c × c
Total number of factors in the product = 9
Number of ways the product can be expressed without exponents
= `(9!)/(2! xx 3! xx 4!)`
= `(9 xx 8 xx 7 xx 6 xx 5 xx 4!)/(2! xx 3! xx 4!)`
= `(9 xx 8 xx 7 xx 6 xx 5)/(2 xx 1 xx 3 xx 2 xx 1)`
= 9 × 4 × 7 × 5
= 1260
APPEARS IN
संबंधित प्रश्न
Evaluate `(n!)/((n-r)!)`, when n = 9, r = 5
Find r if `""^5P_r = ""^6P_(r-1)`
In how many of the distinct permutations of the letters in MISSISSIPPI do the four I’s not come together?
In how many ways can the letters of the word PERMUTATIONS be arranged if the vowels are all together.
Find x in each of the following:
Which of the following are true:
(2 × 3)! = 2! × 3!
In how many ways can three jobs I, II and III be assigned to three persons A, B and C if one person is assigned only one job and all are capable of doing each job?
How many three digit numbers can be formed by using the digits 0, 1, 3, 5, 7 while each digit may be repeated any number of times?
The number of different signals which can be given from 6 flags of different colours taking one or more at a time, is
The number of ways in which 6 men can be arranged in a row so that three particular men are consecutive, is
The number of arrangements of the letters of the word BHARAT taking 3 at a time is
Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 5 and r = 2.
The number of words with or without meaning that can be formed using letters of the word “EQUATION”, with no repetition of letters is:
A student appears in an objective test which contain 5 multiple choice questions. Each question has four choices out of which one correct answer.
How will the answer change if each question may have more than one correct answers?
8 women and 6 men are standing in a line. In how many arrangements will no two men be standing next to one another?
In how many ways 4 mathematics books, 3 physics books, 2 chemistry books and 1 biology book can be arranged on a shelf so that all books of the same subjects are together
Each of the digits 1, 1, 2, 3, 3 and 4 is written on a separate card. The six cards are then laid out in a row to form a 6-digit number. How many of these 6-digit numbers are divisible by 4?
Find the sum of all 4-digit numbers that can be formed using digits 1, 2, 3, 4, and 5 repetitions not allowed?
Find the number of different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are together
