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
How many natural numbers not exceeding 4321 can be formed with the digits 1, 2, 3 and 4, if the digits can repeat?
How many natural numbers less than 1000 can be formed from the digits 0, 1, 2, 3, 4, 5 when a digit may be repeated any number of times?
In how many ways 4 women draw water from 4 taps, if no tap remains unused?
Write the total number of possible outcomes in a throw of 3 dice in which at least one of the dice shows an even number.
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 in a group of n distinct objects, the number of arrangements of 4 objects is 12 times the number of arrangements of 2 objects, then the number of objects is
The number of ways in which 6 men can be arranged in a row so that three particular men are consecutive, is
A 5-digit number divisible by 3 is to be formed using the digits 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways in which this can be done is
The product of r consecutive positive integers is divisible by
The number of words that can be made by re-arranging the letters of the word APURBA so that vowels and consonants are alternate is
In a room there are 12 bulbs of the same wattage, each having a separate switch. The number of ways to light the room with different amounts of illumination is
How many strings are there using the letters of the word INTERMEDIATE, if all the vowels are 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
GARDEN
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
There are 10 persons named P1, P2, P3, ... P10. Out of 10 persons, 5 persons are to be arranged in a line such that in each arrangement P1 must occur whereas P4 and P5 do not occur. Find the number of such possible arrangements.
The number of 5-digit telephone numbers having atleast one of their digits repeated is ______.
The number of permutations of n different objects, taken r at a line, when repetitions are allowed, is ______.
How many words (with or without dictionary meaning) can be made from the letters of the word MONDAY, assuming that no letter is repeated, if
| C1 | C2 |
| (a) 4 letters are used at a time | (i) 720 |
| (b) All letters are used at a time | (ii) 240 |
| (c) All letters are used but the first is a vowel | (iii) 360 |
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 ______.
