Three unbiased coins are tossed. What is the probability of getting at most two heads?

Total number of balls = (8 + 7 + 6) = 21.

Let E	= event that the ball drawn is neither red nor green
	= event that the ball drawn is blue.

∴ n(E) = 7.

∴ P(E) =	n(E)	=	7	=	1	.
	n(S)		21		3

Let number of balls = (6 + 8) = 14.

Number of white balls = 8.

P (drawing a white ball) =	8	=	4	.
	14		7

Let S be the sample space.

Then, n(S) = 52C2 =	(52 x 51)	= 1326.
	(2 x 1)

Let E = event of getting 2 kings out of 4.

∴ n(E) = 4C2 =	(4 x 3)	= 6.
	(2 x 1)

∴ P(E) =	n(E)	=	6	=	1	.
	n(S)		1326		221

Let S be the sample space and E be the event of selecting 1 girl and 2 boys.

Then, n(S)	= Number ways of selecting 3 students out of 25
	= 25C3 `
	= (25 x 24 x 23) (3 x 2 x 1)
	= 2300.

n(E)	= (10C1 x 15C2)
	= [ 10 x (15 x 14) ] (2 x 1)
	= 1050.

∴ P(E) =	n(E)	=	1050	=	21	.
	n(S)		2300		46

In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36.

Then, E

= {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4),      (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1),      (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

∴ n(E) = 27.

∴ P(E) =	n(E)	=	27	=	3	.
	n(S)		36		4

Total number of balls = (2 + 3 + 2) = 7.

Let S be the sample space.

Then, n(S)	= Number of ways of drawing 2 balls out of 7
	= 7C2 `
	= (7 x 6) (2 x 1)
	= 21.

Let E = Event of drawing 2 balls, none of which is blue.

∴ n(E)	= Number of ways of drawing 2 balls out of (2 + 3) balls.
	= 5C2
	= (5 x 4) (2 x 1)
	= 10.

∴ P(E) =	n(E)	=	10	.
	n(S)		21

P (getting a prize) =	10	=	10	=	2	.
	(10 + 25)		35		7

Let T.D. be Re. 1.

Then, B.D. = Rs.	11	= Rs. 1.10.
	10

∴ Sum = Rs.	❨	1.10 x 1	❩	= Rs.	❨	110	❩	= Rs. 11.
		1.10 - 1				10

∴ S.I. on Rs. 11 for 2 years is Rs. 1.10

∴ Rate =	❨	100 x 1.10	❩%	= 5%.
		11 x 2

S.I. on Rs. 1600 = T.D. on Rs. 1680.

∴ Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is on Rs. 1600 at 15%.

∴ Time =	❨	100 x 80	❩year	=	1	year = 4 months.
		1600 x 15			3

T.D.	= B.D. x 100 100 + (R x T)
	= Rs. [ 420 x 100 ] 100 + ❨ 15 x 1 ❩ 3
	= Rs. ❨ 420 x 100 ❩ 105
	= Rs. 400.