Advertisements
Advertisements
प्रश्न
Find x in each of the following:
Advertisements
उत्तर
\[ \frac{1}{4!} + \frac{1}{5!} = \frac{x}{6!}\]
\[ \Rightarrow \frac{1}{4!} + \frac{1}{5(4!)} = \frac{x}{6!}\]
\[ \Rightarrow \frac{5 + 1}{5(4!)} = \frac{x}{6!}\]
\[ \Rightarrow \frac{6}{5!} = \frac{x}{6!}\]
\[ \Rightarrow \frac{6}{5!} = \frac{x}{6 \times 5!}\]
\[ \Rightarrow x = 36\]
APPEARS IN
संबंधित प्रश्न
Evaluate 8!
In how many ways can the letters of the word PERMUTATIONS be arranged if the words start with P and end with S.
In how many ways can the letters of the word PERMUTATIONS be arranged if the there are always 4 letters between P and S?
Find x in each of the following:
If three six faced die each marked with numbers 1 to 6 on six faces, are thrown find the total number of possible outcomes ?
Find the number of ways in which one can post 5 letters in 7 letter 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 total number of possible outcomes in a throw of 3 dice in which at least one of the dice shows an even number.
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 ?
Write the number of ways in which 6 men and 5 women can dine at a round table if no two women sit together ?
Write the remainder obtained when 1! + 2! + 3! + ... + 200! is divided by 14 ?
The number of six letter words that can be formed using the letters of the word "ASSIST" in which S's alternate with other letters is
How many five digits telephone numbers can be constructed using the digits 0 to 9 If each number starts with 67 with no digit appears more than once?
Find the rank of the word ‘CHAT’ in the dictionary.
Evaluate the following.
`(3! xx 0! + 0!)/(2!)`
The greatest positive integer which divide n(n + 1) (n + 2) (n + 3) for all n ∈ N is:
For all n > 0, nC1 + nC2 + nC3 + …… + nCn is equal to:
Suppose 8 people enter an event in a swimming meet. In how many ways could the gold, silver and bronze prizes be awarded?
A student appears in an objective test which contain 5 multiple choice questions. Each question has four choices out of which one correct answer.
What is the maximum number of different answers can the students give?
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?
How many ways can the product a2 b3 c4 be expressed without exponents?
A coin is tossed 8 times, how many different sequences of heads and tails are possible?
How many strings are there using the letters of the word INTERMEDIATE, if vowels are never 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 distinct 6-digit numbers are there?
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
Find the number of strings that can be made using all letters of the word THING. If these words are written as in a dictionary, what will be the 85th string?
Find the sum of all 4-digit numbers that can be formed using digits 1, 2, 3, 4, and 5 repetitions not allowed?
Choose the correct alternative:
If Pr stands for rPr then the sum of the series 1 + P1 + 2P2 + 3P3 + · · · + nPn is
The number of arrangements of the letters of the word BANANA in which two N's do not appear adjacently is ______.
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.
Using the digits 1, 2, 3, 4, 5, 6, 7, a number of 4 different digits is formed. Find
| C1 | C2 |
| (a) How many numbers are formed? | (i) 840 |
| (b) How many number are exactly divisible by 2? | (i) 200 |
| (c) How many numbers are exactly divisible by 25? | (iii) 360 |
| (d) How many of these are exactly divisible by 4? | (iv) 40 |
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Determine the number of words which have at least one letter repeated.
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 ______.
The number of permutations by taking all letters and keeping the vowels of the word ‘COMBINE’ in the odd places is ______.
Number of words from the letters of the words BHARAT in which B and H will never come together is ______.
