Advertisements
Advertisements
Question
If 28C2r : 24C2r − 4 = 225 : 11, find r.
Advertisements
Solution
We have, 28C2r : 24C2r − 4 = 225 : 11
\[ \Rightarrow \frac{28!}{2r! (28 - 2r)!} \times \frac{(2r - 4)! (28 - 2r)!}{24!} = \frac{225}{11}\]
\[ \Rightarrow \frac{28 \times 27 \times 26 \times 25}{2r (2r - 1) (2r - 2) (2r - 3)} = \frac{225}{11}\]
\[ \Rightarrow 2r (2r - 1) (2r - 2) (2r - 3) = \frac{28 \times 27 \times 26 \times 25 \times 11}{225}\]
\[ \Rightarrow 2r (2r - 1) (2r - 2) (2r - 3) = 28 \times 3 \times 26 \times 11\]
\[ \Rightarrow 2r (2r - 1) (2r - 2) (2r - 3) = 4 \times 7 \times 3 \times 13 \times 2 \times 11\]
\[ \Rightarrow 2r (2r - 1) (2r - 2) (2r - 3) = (2 \times 7) \times 13 \times (3 \times 4) \times 11\]
\[ \Rightarrow 2r (2r - 1) (2r - 2) (2r - 3) = 14 \times 13 \times 12 \times 11\]
\[ \Rightarrow 2r = 14\]
\[ \Rightarrow r = 7\]
APPEARS IN
RELATED QUESTIONS
If nC8 = nC2, find nC2.
How many 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated?
The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabet?
Compute:
(i)\[\frac{30!}{28!}\]
A team consists of 6 boys and 4 girls and other has 5 boys and 3 girls. How many single matches can be arranged between the two teams when a boy plays against a boy and a girl plays against a girl?
How many A.P.'s with 10 terms are there whose first term is in the set {1, 2, 3} and whose common difference is in the set {1, 2, 3, 4, 5}?
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 odd numbers less than 1000 can be formed by using the digits 0, 3, 5, 7 when repetition of digits is not allowed?
How many four digit different numbers, greater than 5000 can be formed with the digits 1, 2, 5, 9, 0 when repetition of digits is not allowed?
If n +2C8 : n − 2P4 = 57 : 16, find n.
If nC4 , nC5 and nC6 are in A.P., then find n.
In how many ways can a football team of 11 players be selected from 16 players? How many of these will
exclude 2 particular players?
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.
How many different selections of 4 books can be made from 10 different books, if
two particular books are always selected;
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.
How many triangles can be obtained by joining 12 points, five of which are collinear?
In how many ways can a committee of 5 persons be formed out of 6 men and 4 women when at least one woman has to be necessarily selected?
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 (i) no girl?
In an examination, a question paper consists of 12 questions divided into two parts i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions?
Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many (i) straight lines
There are 3 letters and 3 directed envelopes. Write the number of ways in which no letter is put in the correct envelope.
Find n if `""^(2"n")"C"_3: ""^"n""C"_2` = 52:3
Find n and r if `""^"n""P"_"r"` = 720 and `""^"n""C"_("n" - "r")` = 120
Find the number of ways of drawing 9 balls from a bag that has 6 red balls, 5 green balls, and 7 blue balls so that 3 balls of every colour are drawn.
There are 3 wicketkeepers and 5 bowlers among 22 cricket players. A team of 11 players is to be selected so that there is exactly one wicketkeeper and at least 4 bowlers in the team. How many different teams can be formed?
Find the number of ways of dividing 20 objects in three groups of sizes 8, 7, and 5.
Four parallel lines intersect another set of five parallel lines. Find the number of distinct parallelograms that can be formed.
Find the value of 15C4
Answer the following:
A question paper has 6 questions. How many ways does a student have to answer if he wants to solve at least one question?
In a small village, there are 87 families, of which 52 families have atmost 2 children. In a rural development programme 20 families are to be chosen for assistance, of which atleast 18 families must have at most 2 children. In how many ways can the choice be made?
We wish to select 6 persons from 8, but if the person A is chosen, then B must be chosen. In how many ways can selections be made?
If nCr – 1 = 36, nCr = 84 and nCr + 1 = 126, then find rC2.
In an examination, a student has to answer 4 questions out of 5 questions; questions 1 and 2 are however compulsory. Determine the number of ways in which the student can make the choice.
15C8 + 15C9 – 15C6 – 15C7 = ______.
To fill 12 vacancies there are 25 candidates of which 5 are from scheduled castes. If 3 of the vacancies are reserved for scheduled caste candidates while the rest are open to all, the number of ways in which the selection can be made is 5C3 × 20C9.
If number of arrangements of letters of the word "DHARAMSHALA" taken all at a time so that no two alike letters appear together is (4a.5b.6c.7d), (where a, b, c, d ∈ N), then a + b + c + d is equal to ______.
The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are alike is ______.
