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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?
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A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of: exactly 3 girls?
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A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of: at least 3 girls?
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A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of: atmost 3 girls?
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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?
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A parallelogram is cut by two sets of m lines parallel to its sides. Find the number of parallelograms thus formed.
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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
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Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many (ii) triangles can be formed by joining them?
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How many different words, each containing 2 vowels and 3 consonants can be formed with 5 vowels and 17 consonants?
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Solve the following systems of linear inequation graphically:
2x + 3y ≤ 6, 3x + 2y ≤ 6, x ≥ 0, y ≥ 0
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Solve the following systems of linear inequation graphically:
2x + 3y ≤ 6, x + 4y ≤ 4, x ≥ 0, y ≥ 0
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Solve the following systems of linear inequations graphically:
x − y ≤ 1, x + 2y ≤ 8, 2x + y ≥ 2, x ≥ 0, y ≥ 0
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Solve the following systems of linear inequations graphically:
x + y ≥ 1, 7x + 9y ≤ 63, x ≤ 6, y ≤ 5, x ≥ 0, y ≥ 0
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Solve the following systems of linear inequations graphically:
2x + 3y ≤ 35, y ≥ 3, x ≥ 2, x ≥ 0, y ≥ 0
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Find the number of ways in which : (a) a selection
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Find the number of ways in which : (b) an arrangement, of four letters can be made from the letters of the word 'PROPORTION'.
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Show that the solution set of the following linear inequations is empty set:
x − 2y ≥ 0, 2x − y ≤ −2, x ≥ 0, y ≥ 0
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How many words can be formed by taking 4 letters at a time from the letters of the word 'MORADABAD'?
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Show that the solution set of the following linear inequations is empty set:
x + 2y ≤ 3, 3x + 4y ≥ 12, y ≥ 1, x ≥ 0, y ≥ 0
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A business man hosts a dinner to 21 guests. He is having 2 round tables which can accommodate 15 and 6 persons each. In how many ways can he arrange the guests?
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