Advertisements
Advertisements
प्रश्न
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 (ii) at least one boy and one girl?
उत्तर
If the team has at least 1 boy and 1 girl, then the number of ways of selecting 5 members
\[= {}^4 C_1 \times^7 C_4 +^4 C_2 \times^7 C_3 + {}^4 C_3 \times^7 C_2 +^4 C_4 \times^7 C_1 \]
\[ = 140 + 210 + 84 + 7 \]
\[ = 441\]
APPEARS IN
संबंधित प्रश्न
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?
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?
Prove that
A coin is tossed five times and outcomes are recorded. How many possible outcomes are there?
In how many ways can an examinee answer a set of ten true/false type questions?
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?
Twelve students complete in a race. In how many ways first three prizes be given?
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 different numbers of six digits each can be formed from the digits 4, 5, 6, 7, 8, 9 when repetition of digits is not allowed?
Evaluate the following:
35C35
If 18Cx = 18Cx + 2, find x.
If 2nC3 : nC2 = 44 : 3, find n.
If 16Cr = 16Cr + 2, find rC4.
A student has to answer 10 questions, choosing at least 4 from each of part A and part B. If there are 6 questions in part A and 7 in part B, in how many ways can the student choose 10 questions?
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?
Determine the number of 5 cards combinations out of a deck of 52 cards if there is exactly one ace in each combination.
Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many (i) straight lines
A tea party is arranged for 16 persons along two sides of a long table with 8 chairs on each side. Four persons wish to sit on one particular side and two on the other side. In how many ways can they be seated?
If 15C3r = 15Cr + 3 , then r is equal to
If nC12 = nC8 , then n =
Three persons enter a railway compartment. If there are 5 seats vacant, in how many ways can they take these seats?
There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two of them is
The number of diagonals that can be drawn by joining the vertices of an octagon is
Among 14 players, 5 are bowlers. In how many ways a team of 11 may be formed with at least 4 bowlers?
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is
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?
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 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.
A bag contains six white marbles and five red marbles. Find the number of ways in which four marbles can be drawn from the bag if two must be white and two red
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?
There are 12 points in a plane of which 5 points are collinear, then the number of lines obtained by joining these points in pairs is 12C2 – 5C2.
If some or all of n objects are taken at a time, the number of combinations is 2n – 1.
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!)`.
To fill 12 vacancies there are 25 candidates of which 5 are from scheduled castes. If 3 of the vacancies are reserved for scheduled caste candidates while the rest are open to all, the number of ways in which the selection can be made is 5C3 × 20C9.
There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsmen and 2 are wicketkeepers. The number of ways, a team of 11 players be selected from them so as to include at least 4 bowlers, 5 batsmen and 1 wicketkeeper, is ______.
The no. of different ways, the letters of the word KUMARI can be placed in the 8 boxes of the given figure so that no row remains empty will be ______.
