Advertisements
Advertisements
प्रश्न
Prove that `""^35"C"_5 + sum_("r" = 0)^4 ""^((39 - "r"))"C"_4` = 40C5
उत्तर
`""^35"C"_5 + sum_("r" = 0)^4 ""^((39 - "r"))"C"_4 = ""^35"C"_5 + ""^((39 - 0))"C"_4 + ""^((39 - 1))"C"_4 + ""^((39 - 2))"C"_4 + ""^((39 - 3))"C"_4 + ""^((39 - 4))"C"_4`
= `""^35"C"_4 + ""^39"C"_4 + ""^38"C"_4 + ""^37"C"_4 + ""^36"C"_4 + ""^35"C"_4` ......(1)
`""^"n""C"_("r" - 1) + ""^"n""C"_"r" = ""^(("n" + 1))"C"_"r"`
(1) ⇒ `""^35"C"_5 + sum_("r" = 0)^4 ""^((39 - "r"))"C"_4`
= (35C5 + 35C4) + 39C4 + 38C4 + 38C4 + 37C4 + 36C4
= `""^((35 + 1))"C"_5 + ""^36"C"_4 + ""^39"C"_4 + ""^38"C"_4 + ""^37"C"_4`
= (36C5 + 36C4) + 39C4 + 38C4 + 37C4
= `""^((36 + 1))"C"_5 + ""^37"C"_4 + ""^39"C"_4 + ""^38"C"_4`
= (37C5 + 37C4) + 39C4 + 38C4
= `""^((37 + 1))"C"_5 + ""^38"C"_4 + ""^39"C"_4`
= (38C5 + 38C4) + 39C4
= 39C4 + 39C4
= `""^((39 + 1))"C"_5`
= 40C5
= R.H.S
APPEARS IN
संबंधित प्रश्न
If nPr = 1680 and nCr = 70, find n and r.
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
If a polygon has 44 diagonals, find the number of its sides.
How many code symbols can be formed using 5 out of 6 letters A, B, C, D, E, F so that the letters
- cannot be repeated
- can be repeated
- cannot be repeated but must begin with E
- cannot be repeated but end with CAB.
The number of 3 letter words that can be formed from the letters of the word ‘NUMBER’ when the repetition is allowed are:
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is:
Prove that if 1 ≤ r ≤ n then `"n" xx ""^(("n" - 1))"C"_("r" - 1) = ""^(("n" - "r" + 1))"C"_("r" - 1)`
A Kabaddi coach has 14 players ready to play. How many different teams of 7 players could the coach put on the court?
There are 15 persons in a party and if each 2 of them shakes hands with each other, how many handshakes happen in the party?
Find the total number of subsets of a set with
[Hint: nC0 + nC1 + nC2 + ... + nCn = 2n] n elements
A trust has 25 members. In how many ways can a President, Vice President and a Secretary be selected?
A committee of 7 peoples has to be formed from 8 men and 4 women. In how many ways can this be done when the committee consists of exactly 3 women?
A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box, if at least one black ball is to be included in the draw?
Choose the correct alternative:
The number of ways in which a host lady invite 8 people for a party of 8 out of 12 people of whom two do not want to attend the party together is
Choose the correct alternative:
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines
Choose the correct alternative:
Number of sides of a polygon having 44 diagonals is ______
Choose the correct alternative:
If 10 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then the total number of points of intersection are
Choose the correct alternative:
`""^(("n" - 1))"C"_"r" + ""^(("n" - 1))"C"_(("r" - 1))` is
Choose the correct alternative:
If nC4, nC5, nC6 are in AP the value of n can be
