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
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 number of ways in which one can post 5 letters in 7 letter boxes ?
Find the total number of ways in which 20 balls can be put into 5 boxes so that first box contains just one ball ?
In how many ways can 4 prizes be distributed among 5 students, when
(i) no student gets more than one prize?
(ii) a student may get any number of prizes?
(iii) no student gets all the prizes?
The number of words that can be formed out of the letters of the word "ARTICLE" so that vowels occupy even places is
The number of arrangements of the word "DELHI" in which E precedes I is
The number of ways to arrange the letters of the word CHEESE are
If the letters of the word KRISNA are arranged in all possible ways and these words are written out as in a dictionary, then the rank of the word KRISNA is
If (n+2)! = 60[(n–1)!], find n
Evaluate the following.
`((3!)! xx 2!)/(5!)`
For all n > 0, nC1 + nC2 + nC3 + …… + nCn is equal to:
A test consists of 10 multiple choice questions. In how many ways can the test be answered if each question has four choices?
A test consists of 10 multiple choice questions. In how many ways can the test be answered if the first four questions have three choices and the remaining have five choices?
In how many ways 3 mathematics books, 4 history books, 3 chemistry books and 2 biology books can be arranged on a shelf so that all books of the same subjects are together.
Find the number of permutations of n different things taken r at a time such that two specific things occur together.
Ten different letters of alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have atleast one letter repeated is ______.
The number of signals that can be sent by 6 flags of different colours taking one or more at a time is ______.
The number of words which can be formed out of the letters of the word ARTICLE, so that vowels occupy the even place is ______.
8-digit numbers are formed using the digits 1, 1, 2, 2, 2, 3, 4, 4. The number of such numbers in which the odd digits do no occupy odd places is ______.
