Business Mathematics and Basic Statistics · Class 11 Commerce
Ch 8Permutations and Combinations — Class 11 Business Mathematics and Basic Statistics, concept-first.
Business Mathematics and Basic Statistics (WBCHSE Class 11 Commerce) begins its treatment of counting techniques with the factorial, the building block every permutation and combination formula in this chapter is built from.
Key concepts
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Factorial of a Number
The factorial of a whole number , written , is the product of every whole number from down to : . It is the building block of every permutation and combination formula.
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How often this chapter’s concepts have been examined — real appearance data, never estimated.
Chapter contents
The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.
Factorial Notation
Business Mathematics and Basic Statistics (WBCHSE Class 11 Commerce) begins its treatment of counting techniques with the factorial, the building block every permutation and combination formula in thi…
Permutations — Meaning and Formula (nPr)
A permutation is an arrangement of a group of objects in a definite ORDER. Placing the same 3 people into the roles of President, Secretary and Treasurer in a different order gives three genuinely dif…
Combinations — Meaning and Formula (nCr)
A combination is a SELECTION of a group of objects where the order of picking does not matter. Choosing 3 students — say Asha, Bina and Chitra — for a committee is the SAME outcome no matter which ord…
Applications — Arrangement and Selection Problems
Every word problem in this chapter reduces to one question: if the same objects were chosen in a different order, would the outcome actually be different?
Exercises
+−Show 5 questionsHide questions5 questions
- Q8Evaluate $\dfrac{7!}{5!\,2!}$.Free
- Q9The word 'COMPUTER' has 8 distinct letters. In how many ways can 4 of its letters be selected and arranged to form a new arrangement of 4 le…Free
- Q10A committee of 2 men and 2 women is to be formed from 4 men and 4 women. In how many ways can this be done?Preview
- Q11Find the number of diagonals of a polygon with 8 sides (an octagon).Preview
- Q12Find the value of $r$ if $^{6}P_{r} = 30$.Preview
More questions
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- Example 1Evaluate: (i) $5!$ (ii) $0! + 1!$.Free
- Example 2Evaluate $^{6}P_{2}$.Free
- Example 3Evaluate $^{8}C_{3}$.Free
- Example 4Verify that $^{7}P_{3} = {}^{7}C_{3} \times 3!$.Preview
- Example 5In how many ways can 5 different books be arranged on a shelf?Preview
- Example 6A committee of 3 students is to be chosen from 6 students. In how many ways can this be done?Preview
- Example 7In how many ways can the letters of the word 'MOBILE' be arranged?Preview