Advertisements
Advertisements
Question
Select the correct answer from the given alternatives.
The number of arrangements of the letters of the word BANANA in which two N's do not appear adjacently
Options
80
60
40
100
Advertisements
Solution
40
Explanation;
Arrange B, A, A, A in `(4!)/(3!)` ways.
These four letters create 5 gaps in which 2N are to be filled, this can be done in 5C2 ways, we do not permute those 2N as they are identical.
Required number = `(4!)/(3!) xx ""^5"C"_2` = 40
APPEARS IN
RELATED QUESTIONS
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""P"_"r" = 1814400` and `""^"n""C"_"r"` = 45, find r.
If 20 points are marked on a circle, how many chords can be drawn?
Find the number of diagonals of an n-shaded polygon. In particular, find the number of diagonals when: n = 10
Find the number of diagonals of an n-shaded polygon. In particular, find the number of diagonals when: n = 15
Ten points are plotted on a plane. Find the number of straight lines obtained by joining these points if no three 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 n, if `""^23"C"_(3"n") = ""^23"C"_(2"n" + 3)`
Find n, if `""^21"C"_(6"n") = ""^21"C"_(("n"^2 + 5)`
Find n, if `""^(2"n")"C"_("r" - 1) = ""^(2"n")"C"_("r" + 1)`
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 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?
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.
Find n if nCn–3 = 84
Find r if 14C2r : 10C2r–4 = 143 : 10
Find the number of ways of selecting a team of 3 boys and 2 girls from 6 boys and 4 girls
Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 10
Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 12
Ten points are plotted on a plane. Find the number of straight lines obtained by joining these points if no three points are collinear
Find the number of triangles formed by joining 12 points if no three points are collinear
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 2 vowels are chosen?
Find n if 21C6n = `""^21"C"_(("n"^2 + 5))`
Find the differences between the greatest values in the following:
15Cr and 11Cr
Select the correct answer from the given alternatives.
A question paper has two parts, A and B, each containing 10 questions. If a student has to choose 8 from part A and 5 from part B, In how many ways can he choose the questions?
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.
A student passes an examination if he secures a minimum in each of the 7 subjects. Find the number of ways a student can fail.
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:
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
If vertices of a parallelogram are respectively (2, 2), (3, 2), (4, 4), and (3, 4), then the angle between diagonals is ______
What is the probability of getting a “FULL HOUSE” in five cards drawn in a poker game from a standard pack of 52-cards?
[A FULL HOUSE consists of 3 cards of the same kind (eg, 3 Kings) and 2 cards of another kind (eg, 2 Aces)]
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 ______.
