Advertisements
Advertisements
प्रश्न
Find n and r if `""^"n""P"_"r"` = 720 and `""^"n""C"_("n" - "r")` = 120
Advertisements
उत्तर
`""^"n""P"_"r"` = 720
∴ `("n"!)/(("n" - "r")!)` = 720 ...(i)
Also, `""^"n""C"_("n" - "r")` = 120
∴ `("n"!)/(("n" - "r")!("n"-"n"+"r")!) = 120`
∴ `("n"!)/("r"!("n" - "r")!)` = 120 ...(ii)
Dividing (i) by (ii), we get
∴ `(("n"!)/(("n"-"r")!))/(("n"!)/("r"!("n"-"r")!))=720/120`
∴ r! = 6
∴ r = 3
Substituting r = 3 in (i), we get
∴ `("n"!)/(("n" - 3)!)` = 720
∴ `("n"("n" - 1)("n" - 2)("n" - 3)!)/(("n" - 3)!)` = 720
∴ n(n – 1)(n – 2) = 10 × 9 × 8
∴ n = 10
APPEARS IN
संबंधित प्रश्न
How many chords can be drawn through 21 points on a circle?
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?
How many different numbers of six digits can be formed from the digits 3, 1, 7, 0, 9, 5 when repetition of digits is not allowed?
Evaluate the following:
14C3
Evaluate the following:
n + 1Cn
If 16Cr = 16Cr + 2, find rC4.
From 4 officers and 8 jawans in how many ways can 6 be chosen (i) to include exactly one officer
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?
Find the number of (i) diagonals
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 the selection be made?
Find the number of ways of selecting 9 balls from 6 red balls, 5 white balls and 5 blue balls if each selection consists of 3 balls of each colour.
5C1 + 5C2 + 5C3 + 5C4 +5C5 is equal to
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to
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 value of 15C4
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.
If nC12 = nC8, then n is equal to ______.
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 ______.
There are 12 balls numbered from 1 to 12. The number of ways in which they can be used to fill 8 places in a row so that the balls are with numbers in ascending or descending order is equal to ______.
From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then, the number of such arrangements is ______.
