Advertisements
Advertisements
प्रश्न
If n + 1C3 = 2 · nC2 , then n =
विकल्प
3
4
5
6
उत्तर
5
\[\ ^{n + 1}{}{C}_3 = 2 \times \ ^{n}{}{C}_2 \]
\[ \Rightarrow \frac{\left( n + 1 \right)!}{3! \left( n - 2 \right)!} = 2 \times \frac{n!}{2! \left( n - 2 \right)!}\]
\[ \Rightarrow \frac{\left( n + 1 \right) n!}{3 \times 2! \left( n - 2 \right)!} = 2 \times \frac{n!}{2! \left( n - 2 \right)!}\]
\[ \Rightarrow n + 1 = 6\]
\[ \Rightarrow n = 5\]
APPEARS IN
संबंधित प्रश्न
Determine n if `""^(2n)C_3 : ""^nC_3 = 12 : 1`
Determine n if `""^(2n)C_3 : ""^nC_3 = 11: 1`
Determine the number of 5 card combinations out of a deck of 52 cards if there is exactly one ace in each combination.
In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?
How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?
A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of:
(i) exactly 3 girls?
(ii) atleast 3 girls?
(iii) atmost 3 girls?
Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.
In a class there are 27 boys and 14 girls. The teacher wants to select 1 boy and 1 girl to represent the class in a function. In how many ways can the teacher make this selection?
A letter lock consists of three rings each marked with 10 different letters. In how many ways it is possible to make an unsuccessful attempt to open the lock?
How many A.P.'s with 10 terms are there whose first term is in the set {1, 2, 3} and whose common difference is in the set {1, 2, 3, 4, 5}?
How many three-digit odd numbers are there?
How many 9-digit numbers of different digits can be formed?
Evaluate the following:
14C3
If nC4 = nC6, find 12Cn.
If 16Cr = 16Cr + 2, find rC4.
There are 10 professors and 20 students out of whom a committee of 2 professors and 3 students is to be formed. Find the number of ways in which this can be done. Further find in how many of these committees:
a particular student is included.
How many different products can be obtained by multiplying two or more of the numbers 3, 5, 7, 11 (without repetition)?
How many different selections of 4 books can be made from 10 different books, if two particular books are never selected?
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.
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?
A committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done? How many of these committees would consist of 1 man and 2 women?
In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
Determine the number of 5 cards combinations out of a deck of 52 cards if there is exactly one ace in each combination.
A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of: at least 3 girls?
How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?
How many words can be formed by taking 4 letters at a time from the letters of the word 'MORADABAD'?
If 20Cr = 20Cr−10, then 18Cr is equal to
If 15C3r = 15Cr + 3 , then r is equal to
There are 13 players of cricket, out of which 4 are bowlers. In how many ways a team of eleven be selected from them so as to include at least two bowlers?
If 43Cr − 6 = 43C3r + 1 , then the value of r is
A lady gives a dinner party for six guests. The number of ways in which they may be selected from among ten friends if two of the friends will not attend the party together is
Find n if `""^6"P"_2 = "n" ""^6"C"_2`
Four parallel lines intersect another set of five parallel lines. Find the number of distinct parallelograms that can be formed.
In how many ways can a football team of 11 players be selected from 16 players? How many of them will include 2 particular players?
A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has no girls
15C8 + 15C9 – 15C6 – 15C7 = ______.
The total number of ways in which six ‘+’ and four ‘–’ signs can be arranged in a line such that no two signs ‘–’ occur together is ______.
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 ______.
