Advertisements
Advertisements
प्रश्न
How many ways can the product a2 b3 c4 be expressed without exponents?
Advertisements
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
if `1/(6!) + 1/(7!) = x/(8!)`, find x
Evaluate `(n!)/((n-r)!)`, when n = 9, r = 5
How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?
In how many ways can the letters of the word PERMUTATIONS be arranged if the there are always 4 letters between P and S?
A customer forgets a four-digits code for an Automatic Teller Machine (ATM) in a bank. However, he remembers that this code consists of digits 3, 5, 6 and 9. Find the largest possible number of trials necessary to obtain the correct code.
A coin is tossed three times and the outcomes are recorded. How many possible outcomes are there? How many possible outcomes if the coin is tossed four times? Five times? n times?
Find the total number of ways in which 20 balls can be put into 5 boxes so that first box contains just one ball ?
Write the number of 5 digit numbers that can be formed using digits 0, 1 and 2 ?
Evaluate `("n"!)/("r"!("n" - "r")!)` when n = 5 and r = 2.
How many numbers lesser than 1000 can be formed using the digits 5, 6, 7, 8, and 9 if no digit is repeated?
Evaluate the following.
`(3! + 1!)/(2^2!)`
Three men have 4 coats, 5 waist coats and 6 caps. In how many ways can they wear them?
8 women and 6 men are standing in a line. In how many arrangements will all 6 men be standing next to one another?
8 women and 6 men are standing in a line. In how many arrangements will no two men be standing next to one another?
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 distinct 6-digit numbers are there?
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?
How many words can be formed with the letters of the word MANAGEMENT by rearranging them?
Three married couples are to be seated in a row having six seats in a cinema hall. If spouses are to be seated next to each other, in how many ways can they be seated? Find also the number of ways of their seating if all the ladies sit together.
Let b1, b2, b3, b4 be a 4-element permutation with bi ∈ {1, 2, 3, .......,100} for 1 ≤ i ≤ 4 and bi ≠ bj for i ≠ j, such that either b1, b2, b3 are consecutive integers or b2, b3, b4 are consecutive integers. Then the number of such permutations b1, b2, b3, b4 is equal to ______.
