Advertisements
Advertisements
प्रश्न
Find the differences between the largest values in the following: `""^14"C"_r "and" ""^12"C"_r`
उत्तर
Use `""^"n""C"_r` has maximum value if,
(a) r = `"n"/2` when n is even
(b) r = `("n" - 1)/2 "or" ("n" + 1)/2` when n is odd
`""^14"C"_r "and" ""^12"C"_r`
Maximum value of `""^14"C"_r "occurs at" r = 14/2` = 7
∴ Maximum value of `""^14"C"_r = ""^14"C"_7`
= `(14 xx 13 xx 12 xx 11 xx 10 xx 9 xx 8)/(7 xx 6 xx 5 xx 4 xx 3 xx 2 xx 1)`
= 3432
Maximum value of `""^12"C"_r "occurs at" r = 12/2` = 6
∴ Maximum value of `""^12"C"_r = ""^12"C"_6`
= `(12 xx 11 xx 10 xx 9 xx 8 xx 7)/(8 xx 7 xx 6 xx 5 xx 4 xx 3 xx 2)`
= 924
∴ The difference between the maximum values of `""^14"C"_r "and" ""^12"C"_r`
= 3432 – 924
= 2508.
APPEARS IN
संबंधित प्रश्न
Find the value of 15C4
Find the value of `""^15"C"_4 + ""^15"C"_5`
Find n if `""^"n""C"_8 = ""^"n""C"_12`
Find n, if `""^(2"n")"C"_("r" - 1) = ""^(2"n")"C"_("r" + 1)`
A group consists of 9 men and 6 women. A team of 6 is to be selected. How many of possible selections will have at least 3 women?
Five students are selected from 11. How many ways can these students be selected if two specified students are selected?
If 20 points are marked on a circle, how many chords can be drawn?
Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 10
There are 20 straight lines in a plane so that no two lines are parallel and no three lines are concurrent. Determine the number of points of intersection
Ten points are plotted on a plane. Find the number of straight lines obtained by joining these points if four points are collinear
Find the number of triangles formed by joining 12 points if no three points are collinear
Find n if 23C3n = 23C2n+3
Find r if 11C4 + 11C5 + 12C6 + 13C7 = 14Cr
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?
Select the correct answer from the given alternatives.
The number of ways in which 5 male and 2 female members of a committee can be seated around a round table so that the two females are not seated together is
Answer the following:
30 objects are to be divided in three groups containing 7, 10, 13 objects. Find the number of distinct ways for doing so.
Answer the following:
There are 4 doctors and 8 lawyers in a panel. Find the number of ways for selecting a team of 6 if at least one doctor must be in the team
Answer the following:
Four parallel lines intersect another set of five parallel lines. Find the number of distinct parallelograms formed
Out of 7 consonants and 4 vowels, the number of words (not necessarily meaningful) that can be made, each consisting of 3 consonants and 2 vowels, is ______.
