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महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता ११ वी

Select the correct answer from the given alternatives. In how many ways 4 boys and 3 girls can be seated in a row so that they are alternate

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प्रश्न

Select the correct answer from the given alternatives.

In how many ways 4 boys and 3 girls can be seated in a row so that they are alternate

पर्याय

  • 12

  • 288

  • 144

  • 256

MCQ
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उत्तर

144

Explanation;

B G B G B G B

4 boys take their seats in 4! ways 

3 girls take their seats in 3! ways

Required number = 4! × 3!

= 24 × 6

= 144

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पाठ 3: Permutations and Combination - Miscellaneous Exercise 3.1 [पृष्ठ ६७]

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बालभारती Mathematics and Statistics 2 (Arts and Science) [English] Standard 11 Maharashtra State Board
पाठ 3 Permutations and Combination
Miscellaneous Exercise 3.1 | Q I. (5) | पृष्ठ ६७

संबंधित प्रश्‍न

Evaluate: 8!


Evaluate: 10! – 6!


Compute: `(12!)/(6!)`


Compute: `(9!)/(3!  6!)`


Compute: `(6! - 4!)/(4!)`


Write in terms of factorial.

5 × 6 × 7 × 8 × 9 × 10


Write in terms of factorial.

3 × 6 × 9 × 12 × 15


Write in terms of factorial.

5 × 10 × 15 × 20


Evaluate : `("n"!)/("r"!("n" - "r")!)` for n = 8, r = 6


Evaluate : `("n"!)/("r"!("n" - "r")!)` for n = 12, r = 12


Evaluate : `("n"!)/("r"!("n" - "r")!)` for n = 15, r = 8


Find n, if `(1!)/("n"!) = (1!)/(4!) - 4/(5!)`


Find n, if (n + 3)! = 110 × (n + 1)!


Find n, if: `((17 - "n")!)/((14 - "n")!)` = 5!


Find n, if: `("n"!)/(3!("n" - 3)!) : ("n"!)/(5!("n" - 5)!)` = 5 : 3


Show that `("n"!)/("r"!("n" - "r")!) + ("n"!)/(("r" - 1)!("n" - "r" + 1)!) = (("n" + 1)!)/("r"!("n" - "r" + 1)!)`


Show that `(9!)/(3!6!) + (9!)/(4!5!) = (10!)/(4!6!)`


Simplify `1/("n"!) - 1/(("n" - 1)!) - 1/(("n" - 2)!)`


Simplify `("n" + 2)/("n"!) - (3"n" + 1)/(("n" + 1)!)`


Simplify `1/(("n" - 1)!) + (1 - "n")/(("n" + 1)!)`


Simplify `1/("n"!) - 3/(("n" + 1)!) - ("n"^2 - 4)/(("n" + 2)!)`


Simplify `("n"^2 - 9)/(("n" + 3)!) + 6/(("n" + 2)!) - 1/(("n" + 1)!)`


Select the correct answer from the given alternatives.

In how many ways can 8 Indians and, 4 American and 4 Englishmen can be seated in a row so that all person of the same nationality sit together?


Select the correct answer from the given alternatives.

Find the number of triangles which can be formed by joining the angular points of a polygon of 8 sides as vertices.


Eight white chairs and four black chairs are randomly placed in a row. The probability that no two black chairs are placed adjacently equals.


Let Tn denote the number of triangles which can be formed using the vertices of a regular polygon of n sides. If Tn + 1 – Tn = 21, then n is equal to ______.


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