Advertisements
Advertisements
प्रश्न
If n +2C8 : n − 2P4 = 57 : 16, find n.
Advertisements
उत्तर
\[\Rightarrow \frac{{}^{n + 2} C_8}{{}^{n - 2} P_4} = \frac{57}{16}\]
\[ \Rightarrow \frac{(n + 2)!}{8! (n - 6)!} \times \frac{(n - 6)!}{(n - 2)!} = \frac{57}{16}\]
\[ \Rightarrow \frac{(n + 2) (n + 1) n (n - 1) (n - 2)!}{8!} \times \frac{1}{(n - 2)!} = \frac{57}{16}\]
\[ \Rightarrow (n + 2) (n + 1) n (n - 1) = \frac{57}{16} \times 8! = \frac{19 \times 3}{16} \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1\]
\[ \Rightarrow (n + 2) (n + 1) n (n - 1) = 143640\]
\[ \Rightarrow (n - 1) n (n + 1) (n + 2) = 19 \times 3 \times 7 \times 6 \times 5 \times 4 \times 3\]
\[ \Rightarrow (n - 1) n (n + 1) (n + 2) = 19 \times (3 \times 7) \times (6 \times 3) \times (4 \times 5)\]
\[ \Rightarrow (n - 1) n (n + 1) (n + 2) = 18 \times 19 \times 20 \times 21\]
\[ \Rightarrow n - 1 = 18\]
\[ \Rightarrow n = 19\]
APPEARS IN
संबंधित प्रश्न
If nC8 = nC2, find nC2.
Determine n if `""^(2n)C_3 : ""^nC_3 = 12 : 1`
Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.
If the different permutations of all the letter of the word EXAMINATION are listed as in a dictionary, how many words are there in this list before the first word starting with E?
It is required to seat 5 men and 4 women in a row so that the women occupy the even places. How many such arrangements are possible?
In a class there are 27 boys and 14 girls. The teacher wants to select 1 boy and 1 girl to represent the class in a function. In how many ways can the teacher make this selection?
There are four parcels and five post-offices. In how many different ways can the parcels be sent by registered post?
There are 6 multiple choice questions in an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next three have 2 each?
There are 5 books on Mathematics and 6 books on Physics in a book shop. In how many ways can a students buy : (i) a Mathematics book and a Physics book (ii) either a Mathematics book or a Physics book?
How many three-digit numbers are there?
How many four-digit numbers can be formed with the digits 3, 5, 7, 8, 9 which are greater than 7000, if repetition of digits is not allowed?
Since the number has to be greater than 8000, the thousand's place can be filled by only two digits, i.e. 8 and 9.
Now, the hundred's place can be filled with the remaining 4 digits as the repetition of the digits is not allowed.
The ten's place can be filled with the remaining 3 digits.
The unit's place can be filled with the remaining 2 digits.
Total numbers that can be formed = `2xx4xx3xx2=48`
How many different numbers of six digits each can be formed from the digits 4, 5, 6, 7, 8, 9 when repetition of digits is not allowed?
If nC4 = nC6, find 12Cn.
If 15C3r = 15Cr + 3, find r.
How many different boat parties of 8, consisting of 5 boys and 3 girls, can be made from 25 boys and 10 girls?
There are 10 professors and 20 students out of whom a committee of 2 professors and 3 students is to be formed. Find the number of ways in which this can be done. Further find in how many of these committees:
a particular student is included.
From 4 officers and 8 jawans in how many ways can 6 be chosen (i) to include exactly one officer
There are 10 points in a plane of which 4 are collinear. How many different straight lines can be drawn by joining these points.
Find the number of diagonals of , 1.a hexagon
In a village, there are 87 families of which 52 families have at most 2 children. In a rural development programme, 20 families are to be helped chosen for assistance, of which at least 18 families must have at most 2 children. In how many ways can the choice be made?
How many words can be formed by taking 4 letters at a time from the letters of the word 'MORADABAD'?
If 20Cr = 20Cr + 4 , then rC3 is equal to
There are 12 points in a plane. The number of the straight lines joining any two of them when 3 of them are collinear, is
Among 14 players, 5 are bowlers. In how many ways a team of 11 may be formed with at least 4 bowlers?
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is
Find n and r if `""^"n""P"_"r"` = 720 and `""^"n""C"_("n" - "r")` = 120
The value of `(""^9"C"_0 + ""^9"C"_1) + (""^9"C"_1 + ""^9"C"_2) + ... + (""^9"C"_8 + ""^9"C"_9)` is ______
If nCr – 1 = 36, nCr = 84 and nCr + 1 = 126, then find rC2.
A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if they must all be of the same colour.
A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has no girls
There are 12 points in a plane of which 5 points are collinear, then the number of lines obtained by joining these points in pairs is 12C2 – 5C2.
A scientific committee is to be formed from 6 Indians and 8 foreigners, which includes at least 2 Indians and double the number of foreigners as Indians. Then the number of ways, the committee can be formed is ______.
A badminton club has 10 couples as members. They meet to organise a mixed double match. If each wife refers to p artner as well as oppose her husband in the match, then the number of different ways can the match off will be ______.
There are 12 persons seated in a line. Number of ways in which 3 persons can be selected such that atleast two of them are consecutive, is ______.
Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear is ______.
The number of numbers between 2,000 and 5,000 that can be formed with the digits 0, 1, 2, 3, 4, (repetition of digits is not allowed) and are multiple of 3 is?
