Advertisements
Advertisements
प्रश्न
Find r if `""^11"C"_4 + ""^11"C"_5 + ""^12"C"_6 + ""^13"C"_7 = ""^14"C"_"r"`
उत्तर
Use `""^"n""C"_"r" + ""^"n""C"_("r" - 1) = ""^("n" + 1)"C"_"r"`
∴ `""^11"C"_4 + ""^11"C"_5 + ""^12"C"_6 + ""^13"C"_7 = ""^14"C"_"r"`
∴ `(""^12"C"_5 + ""^12"C"_6) + ""^13"C"_7 = ""^14"C"_"r"`
∴ `(""^13"C"_6 + ""^13"C"_7) = ""^14"C"_"r"`
∴ `""^14"C"_7 = ""^14"C"_"r"`
If nCx = nCy, then either x = y or x = n − y
∴ r = 7 or r = 14 − 7 = 7
APPEARS IN
संबंधित प्रश्न
Find the value of 15C4
If 20 points are marked on a circle, how many chords can be drawn?
Find n, if `""^(2"n")"C"_("r" - 1) = ""^(2"n")"C"_("r" + 1)`
find the value of `sum_("r" = 1)^4 ""^(21 - "r")"C"_4 + ""^17"C"_5`
Find the differences between the largest values in the following: `""^14"C"_r "and" ""^12"C"_r`
Find the differences between the largest values in the following: `""^13"C"_r "and" ""^8"C"_r`
In how many ways can a boy invite his 5 friends to a party so that at least three join the party?
A committee of 10 persons is to be formed from a group of 10 women and 8 men. How many possible committees will have at least 5 women? How many possible committees will have men in the majority?
A question paper has two sections. section I has 5 questions and section II has 6 questions. A student must answer at least two questions from each section among 6 questions he answers. How many different choices does the student have in choosing questions?
Find n and r if nPr = 720 and nCn–r = 120
If nPr = 1814400 and nCr = 45, find n+4Cr+3
After a meeting, every participant shakes hands with every other participants. If the number of handshakes is 66, find the number of participants in the meeting.
Find n if nC8 = nC12
Find n if 23C3n = 23C2n+3
Find n if 21C6n = `""^21"C"_(("n"^2 + 5))`
A committee of 10 persons is to be formed from a group of 10 women and 8 men. How many possible committees will have at least 5 women? How many possible committees will have men in majority?
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:
Nine friends decide to go for a picnic in two groups. One group decides to go by car and the other group decides to go by train. Find the number of different ways of doing so if there must be at least 3 friends in each group.
Answer the following:
Find the number of ways of dividing 20 objects in three groups of sizes 8, 7 and 5
Answer the following:
Four parallel lines intersect another set of five parallel lines. Find the number of distinct parallelograms formed
