distribute 10 carrots in 2 bags => (10 + 2 - 1)C(2 -1) = 11distribute 6 radishes in 2 bags => (6 + 2 - 1)C(2 - 1) = 7total = 11 * 7 = 77But the red bag is empty in one case and the green bag in another.So 77 - 2 = 75
Petya's mother sends him to the market with a red and a green bag to buy 10 carrots and 6 radishes.On his way home, Petya distributes the vegetables into 2 bags in such a way that no bag is empty. In how many ways can he do this?
75.
Use formula for DIVISION OF IDENTICAL OBJECTS INTO GROUPS
(n+r-1) C (r-1) for raddishes n carrots seperately n multiply them...
11*7=77
Remove 2 cases in which either of the bag is empty... 77-2=75.
A coin with diameter 1 cm rolls around the outside of a regular hexagon with edges of length 1 cm until it returns to its original position. In centimeters, what is the length of the path traced out by the centre of the coin?
1. Given a set A={1,2,3,4,5} B= {a,b,c} f:A->B Find the :
a. Total Number of functions b. Number of Surjective functions c. Number of into functions d. Number of bijective functions e. Number of injective functions
A coin with diameter 1 cm rolls around the outside of a regular hexagon with edges of length 1 cm until it returns to its original position. In centimeters, what is the length of the path traced out by the centre of the coin?(1) 6 +pi/2(2) 12 + pi (3) 6 + pi (4) 12 + 2pi (5) 6 + 2pi
3) 6 + pi
r = 0.5 s = 1
path traced = perimeter of hexagon + 6 * 60/360 * 0.5 * 2pi = 6 + pi
1. Given a set A={1,2,3,4,5} B= {a,b,c} f:A->BFind the :a. Total Number of functionsb. Number of Surjective functions c. Number of into functionsd. Number of bijective functionse. Number of injective functionsAny idea how to do this ??
Total Number of functions = 3^5
Number of Surjective functions = E(r=1 to n)(-1)^(n-r) *C(n,r)*r^m =(-1)^2*3c1*1^5+(-1)^1*3c2*2^5+(-1)^0*3c3*3^5 =3 - 96 + 243 =150
Number of into functions = total - onto = 3^5-150 = 97
The path traced will run parallel to the sides of the hexagon at a distance of 0.5 The centre covers an arc of 60 degrees to change the direction of the path at every vertex of the hexagon.
Total Number of functions = 3^5Number of Surjective functions = E(r=1 to n)(-1)^(n-r) *C(n,r)*r^m=(-1)^2*3c1*1^5+(-1)^1*3c2*2^5+(-1)^0*3c3*3^5=3 - 96 + 243=150Number of into functions = total - onto = 3^5-150 = 97Number of bijective functions = 0Number of injective function = 0
Thanks so much sir. But could you please explain the concept behind this ? I'm sorry if its really basic.. but I couldn't find solutions to this or concept explanation anywhere 😞 Also, pls explain what are the conditions in which such functions exist / don't exist
