The toys are different; The boxes are identical
If none of the boxes is to remain empty, then we can pack the toys in one of the following ways
a. 2, 2, 1
b. 3, 1, 1
Case a. Number of ways of achieving the first option 2 - 2 - 1
Two toys out of the 5 can be selected in ways. Another 2 out of the remaining 3 can be selected in ways and the last toy can be selected in way.
However, as the boxes are identical, the two different ways of selecting which box holds the first two toys and which one holds the second set of two toys will look the same. Hence, we need to divide the result by 2
Therefore, total number of ways of achieving the 2 - 2 - 1 option is ways = 15 ways
Case b. Number of ways of achieving the second option 3 - 1 - 1
Three toys out of the 5 can be selected in ways. As the boxes are identical, the remaining two toys can go into the two identical looking boxes in only one way.
Therefore, total number of ways of getting the 3 - 1 - 1 option is = 10 = 10 ways.
Total ways in which the 5 toys can be packed in 3 identical boxes
= number of ways of achieving Case a + number of ways of achieving Case b= 15 + 10 = 25 ways.
Given in the question,
Price of 6 toys is Rs. 264.37.
? Price of 1 toys is Rs. 264.37/ 6 .
? Price of 5 toys is Rs. 264.37 x 5 / 6 .
? Price of 5 toys is Rs. 44 x 5 .
? Price of 5 toys is Rs. 220.
Ratio of the speeds of A and B = 5 : 3
Thus, in a race of 5m, A gains 2 m over B.
2 m are gained by A in a race of 5 m.
40 m will be gained by A in a race of (5/2) x 40 m = 100 m
? Winning post is 100 m away from the starting point.
Velocity of stream = (downstream velocity - upstream velocity)/2
= (60/10 - 60/30)/2
= 2 km/hr
Let their ages one years ago be 4x and 3x years.
? (4x + 2)/(3x + 2) = 5 / 4
? 4(4x + 2) = 5(3x + 2)
? x = 2
? Sum of their present ages = (4x + 1) + (3x + 1) = 16 years
Required number
= 786 x 964 = 757704
Let the C.P. be Rs. x
Then 2(69 - x) / 100 = (78 - x) / 100
? 138 - 2x = 78 - x
? x = 60
? C.P. = Rs. 60
Score of A = 100 points
Score of B = 65 points
? A can give (100 - 65 ) = 35 points to B.
Given expression = log 8 + log (1/8)
= log 8 x (1/8)
= log 1
= 0
Let N = 312 x 28
? log N = 12 x log3 + 8 x log 2
? log N = 12 x 0.47712 + 8 x 0.30103
? log N = 8.13368
? No.of digits = 8 + 1 = 9
Place value of 5 in 65231 = 5 x 1000
= 5000
Face value = 5
required product = 5000 x 5 = 25000
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