Advertisements
Advertisements
Question
If some or all of n objects are taken at a time, the number of combinations is 2n – 1.
Options
True
False
Advertisements
Solution
This statement is True.
Explanation:
When some or all objects, taken at a time, then the number of selection will be
nC1 + nC2 + nC3 + ... + nCn
= 2n – 1 .....[∵ nC0 + nC1 + nC2 + ... + nCn = 2n]
APPEARS IN
RELATED QUESTIONS
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 6-digit numbers can be formed from the digits 0, 1, 3, 5, 7 and 9 which are divisible by 10 and no digit is repeated?
Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.
From a class of 25 students, 10 are to be chosen for an excursion party. There are 3 students who decide that either all of them will join or none of them will join. In how many ways can the excursion party be chosen?
There are 6 multiple choice questions in an examination. How many sequences of answers are possible, if the first three questions have 4 choices each and the next three have 2 each?
How many different five-digit number licence plates can be made if
the first-digit cannot be zero, but the repetition of digits is allowed?
Evaluate the following:
35C35
If 8Cr − 7C3 = 7C2, find r.
If n +2C8 : n − 2P4 = 57 : 16, find n.
If nC4 , nC5 and nC6 are in A.P., then find n.
If 2nC3 : nC2 = 44 : 3, find n.
If α = mC2, then find the value of αC2.
How many different boat parties of 8, consisting of 5 boys and 3 girls, can be made from 25 boys and 10 girls?
In how many ways can a football team of 11 players be selected from 16 players? How many of these will
exclude 2 particular players?
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 professor is included.
From a class of 12 boys and 10 girls, 10 students are to be chosen for a competition; at least including 4 boys and 4 girls. The 2 girls who won the prizes last year should be included. In how many ways can the selection be made?
From 4 officers and 8 jawans in how many ways can 6 be chosen (i) to include exactly one officer
How many triangles can be obtained by joining 12 points, five of which are collinear?
In how many ways can one select a cricket team of eleven from 17 players in which only 5 persons can bowl if each cricket team of 11 must include exactly 4 bowlers?
Find the number of ways in which : (a) a selection
If 20Cr = 20Cr−10, then 18Cr is equal to
If 20Cr = 20Cr + 4 , then rC3 is equal to
If nC12 = nC8 , then n =
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
If n + 1C3 = 2 · nC2 , then n =
Find n if `""^(2"n")"C"_3: ""^"n""C"_2` = 52:3
Find the number of ways of drawing 9 balls from a bag that has 6 red balls, 5 green balls, and 7 blue balls so that 3 balls of every colour are drawn.
There are 20 straight lines in a plane so that no two lines are parallel and no three lines are concurrent. Determine the number of points of intersection.
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?
Find the number of ways of dividing 20 objects in three groups of sizes 8, 7, and 5.
In how many ways can the letters of the word 'IMAGE' be arranged so that the vowels should always occupy odd places?
A bag contains 5 black and 6 red balls. Determine the number of ways in which 2 black and 3 red balls can be selected from the lot.
If nC12 = nC8, then n is equal to ______.
A committee of 6 is to be chosen from 10 men and 7 women so as to contain atleast 3 men and 2 women. In how many different ways can this be done if two particular women refuse to serve on the same committee ______.
The number of positive integers satisfying the inequality `""^(n+1)C_(n-2) - ""^(n+1)C_(n-1) ≤ 100` is ______.
There are (n + 1) white and (n + 1) black balls each set numbered 1 to (n + 1). The number of ways in which the balls can be arranged in row so that the adjacent balls are of different colours is ______.
