Advertisements
Advertisements
प्रश्न
In how many ways can a committee of 5 persons be formed out of 6 men and 4 women when at least one woman has to be necessarily selected?
Advertisements
उत्तर
5 persons are to be selected out of 6 men and 4 women. At least, one woman has to be selected in all cases.
\[\text{Required number of ways} =^4 C_1 \times^6 C_4 + {}^4 C_2 \times^6 C_3 + {}^4 C_3 \times^6 C_2 +^4 C_4 \times^6 C_1 \]
\[ = 60 + 120 + 60 + 6 \]
\[ = 246\]
APPEARS IN
संबंधित प्रश्न
How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed from the letters of the word DAUGHTER?
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?
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?
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?
Compute:
From among the 36 teachers in a college, one principal, one vice-principal and the teacher-incharge are to be appointed. In how many ways can this be done?
How many three-digit odd numbers are there?
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?
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?
If nC4 = nC6, find 12Cn.
If 28C2r : 24C2r − 4 = 225 : 11, find r.
If nC4 , nC5 and nC6 are in A.P., then find n.
If 16Cr = 16Cr + 2, find rC4.
How many different selections of 4 books can be made from 10 different books, if two particular books are never selected?
Find the number of diagonals of (ii) a polygon of 16 sides.
How many triangles can be obtained by joining 12 points, five of which are collinear?
Find the number of (i) diagonals
Find the number of ways in which : (a) a selection
There are 3 letters and 3 directed envelopes. Write the number of ways in which no letter is put in the correct envelope.
If 20Cr = 20Cr + 4 , then rC3 is equal to
If mC1 = nC2 , then
If nCr + nCr + 1 = n + 1Cx , then x =
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is
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.
Five students are selected from 11. How many ways can these students be selected if two specified students are not selected?
A student finds 7 books of his interest, but can borrow only three books. He wants to borrow 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.
Find the value of 15C4 + 15C5
In how many ways a committee consisting of 3 men and 2 women, can be chosen from 7 men and 5 women?
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 nCr – 1 = 36, nCr = 84 and nCr + 1 = 126, then find rC2.
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 they can be of any colour
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?
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 at least one boy and one girl
Three balls are drawn from a bag containing 5 red, 4 white and 3 black balls. The number of ways in which this can be done if at least 2 are red is ______.
A box contains 2 white balls, 3 black balls and 4 red balls. The number of ways three balls be drawn from the box if at least one black ball is to be included in the draw is ______.
There are 3 books on Mathematics, 4 on Physics and 5 on English. How many different collections can be made such that each collection consists of:
| C1 | C2 |
| (a) One book of each subject; | (i) 3968 |
| (b) At least one book of each subject: | (ii) 60 |
| (c) At least one book of English: | (iii) 3255 |
The value of `""^50"C"_4 + sum_("r" = 1)^6 ""^(56 - "r")"C"_3` 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 ______.
