Advertisements
Advertisements
प्रश्न
Evaluate each of the following:
Advertisements
उत्तर
\[\ {}^{10} P_4 = \frac{10!}{(10 - 4)!} \]
\[ = \frac{10!}{6!}\]
\[ = \frac{10(9)(8)(7)(6!)}{6!}\]
\[ = 10 \times 9 \times 8 \times 7 \]
\[ = 5040\]
APPEARS IN
संबंधित प्रश्न
How many 4-digit numbers are there with no digit repeated?
From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person cannot hold more than one position?
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?
Find x in each of the following:
Which of the following are true:
(2 × 3)! = 2! × 3!
How many numbers of six digits can be formed from the digits 0, 1, 3, 5, 7 and 9 when no digit is repeated? How many of them are divisible by 10 ?
If three six faced die each marked with numbers 1 to 6 on six faces, are thrown find the total number of possible outcomes ?
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?
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?
Evaluate each of the following:
P(6, 4)
In how many ways 4 women draw water from 4 taps, if no tap remains unused?
Write the number of all possible words that can be formed using the letters of the word 'MATHEMATICS'.
Write the number of numbers that can be formed using all for digits 1, 2, 3, 4 ?
The number of words from the letters of the word 'BHARAT' in which B and H will never come together, is
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
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 different ways in which 8 persons can stand in a row so that between two particular persons A and B there are always two persons, 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?
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!)! xx 2!)/(5!)`
If `""^10"P"_("r" - 1)` = 2 × 6Pr, find r
Suppose 8 people enter an event in a swimming meet. In how many ways could the gold, silver and bronze prizes be awarded?
Determine the number of permutations of the letters of the word SIMPLE if all are taken at a time?
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 question number n has n + 1 choices?
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 strings are there using the letters of the word INTERMEDIATE, if all the vowels are together
How many strings are there using the letters of the word INTERMEDIATE, if no two vowels are together
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?
In how many ways can 5 children be arranged in a line such that two particular children of them are never together.
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
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 ______.
Five boys and five girls form a line. Find the number of ways of making the seating arrangement under the following condition:
| C1 | C2 |
| (a) Boys and girls alternate: | (i) 5! × 6! |
| (b) No two girls sit together : | (ii) 10! – 5! 6! |
| (c) All the girls sit together | (iii) (5!)2 + (5!)2 |
| (d) All the girls are never together : | (iv) 2! 5! 5! |
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 |
