Science stream knowledge

 5 Most important question regarding permutations and combinations with deep concept.

1.Find out the number of way in which 2 boys and 3 girls salected out of 5 boys and 7 girls.

Solution: Given that we have 5 boys and 7 girls.

So the number of way salect 3 boys out of 5 boys = 5c2 =5!/(5-2)!×2! = 5!/3!×2! = 120/6×2 = 10

Similarly the number of way to salect 3 girls out of 7 girls = 7c3 = 7!/(7-3)!×3! = 7!/4!×3! = 5040/24×6 = 35

Hence the total number of way to salect 2 boys and 3 girls = 10×35 = 350.

2.Find out the number of way in which 3 boys and 4 girls salected out of 5 boys and 7 girls.

Solution: Given that we have 5 boys and 7 girls.

So the number of way salect 3 boys out of 5 boys = 5c3 =5!/(5-3)!×3! = 5!/2!×3! = 120/2×6 = 10

Similarly the number of way to salect 4 girls out of 7 girls = 7c4 = 7!/(7-4)!×4! = 7!/3!×4! = 5040/6×24 = 35

Hence the total number of way to salect 3 boys and 4 girls = 10×35 = 350.

3.Find out the number of way in which 4 boys and 5 girls salected out of 5 boys and 7 girls.

Solution: Given that we have 5 boys and 7 girls.

So the number of way salect 4 boys out of 5 boys  = 5c4 =5!/(5-4)!×4! = 5!/1!×4! = 120/1×24 = 5

Similarly the number of way to salect 5 girls out of 7 girls = 7c5 = 7!/(7-5)!×5! = 7!/2!×5! = 5040/2×120 = 21

Hence the total number of way to salect 4  boys and 5 girls = 5×21 = 105.

4.Find out the number of way in which 3 boys and 4 girls salected out of 6 boys and 7 girls.

Solution: Given that we have 6 boys and 7 girls.

So the number of way salect 3 boys out of 6 boys = 6c3 =6!/(6-3)!×3! = 6!/3!×3! = 720/6×6 = 20

Similarly the number of way to salect 4 girls out of 7 girls = 7c4 = 7!/(7-4)!×4! = 7!/3!×4! = 5040/6×24 = 35

Hence the total number of way to salect 3 boys and 4 girls = 20×35 = 700.

5.Find out the number of way in which 3 boys and 4 girls salected out of 8 boys and 8 girls.

Solution: Given that we have 8 boys and 8 girls.

So the number of way salect 3 boys out of 8 boys = 8c3 =8!/(8-3)!×3! = 8!/5!×3! = 40320/120×6 = 56

Similarly the number of way to salect 4 girls out of 8 girls = 8c4 = 8!/(8-4)!×4! = 8!/4!×4! = 40320/24×24 = 70

Hence the total number of way to salect 3 boys and 4 girls = 56×70 = 3920.

I hope friends these questions helpful for you. Please share these questions.