Advertisements
Advertisements
Question
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}?
Solution
Number of ways of selecting the first term from the set {1, 2, 3} = 3
Corresponding to each of the selected first terms, the number of ways of selecting the common difference from the set {1, 2, 3, 4, 5} = 5
∴ Total number of AP's that can be formed = 3\[\times\]5 = 15
APPEARS IN
RELATED QUESTIONS
In how many ways can one select a cricket team of eleven from 17 players in which only 5 players can bowl if each cricket team of 11 must include exactly 4 bowlers?
Compute:
(i)\[\frac{30!}{28!}\]
Prove that
In how many ways can an examinee answer a set of ten true/false type questions?
Given 7 flags of different colours, how many different signals can be generated if a signal requires the use of two flags, one below the other?
Twelve students complete in a race. In how many ways first three prizes be given?
How many three-digit numbers are there with no digit repeated?
How many four-digit numbers can be formed with the digits 3, 5, 7, 8, 9 which are greater than 7000, if repetition of digits is not allowed?
How many 3-digit numbers are there, with distinct digits, with each digit odd?
If 18Cx = 18Cx + 2, find x.
If nC4 , nC5 and nC6 are in A.P., then find n.
If 2nC3 : nC2 = 44 : 3, find n.
If 16Cr = 16Cr + 2, find rC4.
How many different selections of 4 books can be made from 10 different books, if
there is no restriction;
How many different selections of 4 books can be made from 10 different books, if two particular books are never selected?
There are 10 points in a plane of which 4 are collinear. How many different straight lines can be drawn by joining these points.
Find the number of (i) diagonals
In how many ways can a team of 3 boys and 3 girls be selected from 5 boys and 4 girls?
In an examination, a question paper consists of 12 questions divided into two parts i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions?
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'?
Find the number of combinations and permutations of 4 letters taken from the word 'EXAMINATION'.
There are 3 letters and 3 directed envelopes. Write the number of ways in which no letter is put in the correct envelope.
If C (n, 12) = C (n, 8), then C (22, n) is equal to
5C1 + 5C2 + 5C3 + 5C4 +5C5 is equal to
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 and r if `""^"n""P"_"r"` = 720 and `""^"n""C"_("n" - "r")` = 120
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?
Five students are selected from 11. How many ways can these students be selected if two specified students are not selected?
Four parallel lines intersect another set of five parallel lines. Find the number of distinct parallelograms that can be formed.
Find the value of 15C4
Answer the following:
A question paper has 6 questions. How many ways does a student have to answer if he wants to solve at least one question?
We wish to select 6 persons from 8, but if the person A is chosen, then B must be chosen. In how many ways can selections be made?
If 20 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, in how many points will they intersect each other?
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?
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is ______.
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 ______.
Eighteen guests are to be seated, half on each side of a long table. Four particular guests desire to sit on one particular side and three others on other side of the table. The number of ways in which the seating arrangements can be made is `(11!)/(5!6!) (9!)(9!)`.
A candidate is required to answer 7 questions out of 12 questions which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. He can choose the seven questions in 650 ways.
