It is explicitly given that all the 4 black balls are different, all the 3 red balls are different and all the 5 blue balls are different. Hence this is a case where all are distinct objects.
Initially let's find out the number of ways in which we can select the black balls. Note that at least 1 black ball must be included in each selection.
Hence, we can select 1 black ball from 4 black balls
or 2 black balls from 4 black balls.
or 3 black balls from 4 black balls.
or 4 black balls from 4 black balls.
Hence, number of ways in which we can select the black balls
= 4C1 + 4C2 + 4C3 + 4C4
=
........(A)
Now let's find out the number of ways in which we can select the red balls. Note that at least 1 red ball must be included in each selection.
Hence, we can select 1 red ball from 3 red balls
or 2 red balls from 3 red balls
or 3 red balls from 3 red balls
Hence, number of ways in which we can select the red balls
= 3C1 + 3C2 + 3C3
=
........(B)
Hence, we can select 0 blue ball from 5 blue balls (i.e, do not select any blue ball. In this case, only black and red balls will be there)
or 1 blue ball from 5 blue balls
or 2 blue balls from 5 blue balls
or 3 blue balls from 5 blue balls
or 4 blue balls from 5 blue balls
or 5 blue balls from 5 blue balls.
Hence, number of ways in which we can select the blue balls
= 5C0 + 5C1 + 5C2 + ? + 5C5
=
..............(C)
From (A), (B) and (C), required number of ways
=
22020 ÷ 0.011 = 2001818.181 ? 2000000
In 12 h, they are at a right angles, 22 times.
So, in 24 h, they are at right angles, 44 times.
P.W. = | 100 x T.D. | = | 100 x 168 | = 600. |
R x T | 14 x 2 |
∴ Sum = (P.W. + T.D.) = Rs. (600 + 168) = Rs. 768.
Each number is double the preceding one plus 1. So, the next number is (255 x 2) + 1 = 511.
Here, n(5) = {a, e, i,o, u}
and E = Event of selecting the vowel i = {i}
? P(E)= n(E)/n(S) = 1/5
? 90A/100 = 30B/100 = (30/100) x AC/100
? C = 100 x (100/30) x (90/100) = 300
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