Advertisements
Advertisements
Question
How many ways can the product a2 b3 c4 be expressed without exponents?
Advertisements
Solution
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
RELATED QUESTIONS
In how many ways can 5 different balls be distributed among three boxes?
There are 10 lamps in a hall. Each one of them can be switched on independently. Find the number of ways in which the hall can be illuminated ?
Evaluate each of the following:
8P3
Write the number of ways in which 7 men and 7 women can sit on a round table such that no two women sit together ?
The number of five-digit telephone numbers having at least one of their digits repeated is
The number of ways in which the letters of the word ARTICLE can be arranged so that even places are always occupied by consonants is
The possible outcomes when a coin is tossed five times:
For all n > 0, nC1 + nC2 + nC3 + …… + nCn is equal to:
Determine the number of permutations of the letters of the word SIMPLE if all are taken at a time?
How many strings can be formed from the letters of the word ARTICLE, so that vowels occupy the even places?
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
How many strings are there using the letters of the word INTERMEDIATE, if vowels are never together
If the letters of the word GARDEN are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, then find the ranks of the words
DANGER
Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?
Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.
Find the number of different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are together
The total number of 9 digit numbers which have all different digits is ______.
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 ______.
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 ______.
