Advertisements
Advertisements
Question
Find the differences between the largest values in the following: `""^15"C"_r "and" ""^11"C"_r`
Solution
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
`""^15"C"_r "and" ""^11"C"_r`
Maximum value of `""^15"C"_r "occurs at" r = 14/2 = 7 "or r = 16/2` = 8
∴ Maximum value of `""^15"C"_r = ""^15"C"_7 = ""^15"C"_8`
= `(15 xx 14 xx 13 xx 12 xx 11 xx 10 xx 9)/(7 xx 6 xx 5 xx 4 xx 3 xx 2 xx 1)`
= 6435
Maximum value of `""^11"C"_r "occurs at" r = 10/2 = 5 "or" r = 12/2` = 6
∴ Maximum value of `""^11"C"_r = ""^11"C"_5 = ""^11"C"_6`
`""^11"C"_r = ""^11"C"_5 = (11 xx 10 xx 9 xx 8 xx 7)/(5 xx 4 xx 3 xx 2 xx 1)`
= 462
∴ The difference between the maximum values of `""^15"C"_r "and" ""^11"C"_r`
= 6435 – 462
= 5973.
APPEARS IN
RELATED QUESTIONS
Find the value of `""^15"C"_4 + ""^15"C"_5`
Find the value of `""^20"C"_16 - ""^19"C"_16`
Find r if `""^14"C"_(2"r"): ""^10"C"_(2"r" - 4)` = 143:10
Find n and r if `""^"n""C"_("r" - 1): ""^"n""C"_"r": ""^"n""C"_("r" + 1)` = 20:35:42
If `""^"n""C"_("r" - 1)` = 6435, `""^"n""C"_"r"` = 5005, `""^"n""C"_("r" + 1)` = 3003, find `""^"r""C"_5`.
Find the number of triangles formed by joining 12 points if four points are collinear.
A word has 8 consonants and 3 vowels. How many distinct words can be formed if 4 consonants and 12 vowels are chosen?
Find x if `""^"n""P"_"r" = "x" ""^"n""C"_"r"`
Find the differences between the largest values in the following: `""^14"C"_r "and" ""^12"C"_r`
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?
Find n and r if nPr = 720 and nCn–r = 120
If nCr–1 = 6435, nCr = 5005, nCr+1 = 3003, find rC5
Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 10
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
In how many ways can a boy invite his 5 friends to a party so that at least three join the party?
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?
Answer the following:
A student finds 7 books of his interest but can borrow only three books. He wants to borrow the Chemistry part-II book only if Chemistry Part-I can also be borrowed. Find the number of ways he can choose three books that he wants to borrow.
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 ______.
