Answer:
The correct options are;
A. 120
B. 34
Explanation:
The given parameters are;
Required to find how many of the permutations of 1, 2, 3, 4, 5, 6, have 1, 2, 3 arranged one after the other in the given order
Requirement to arrange 6 digits, 1, 2, 3, 4, 5, 6 in the order such that 1, 2, and 3 always appear in turn, they are as follows
When the first digit is 1, and the 2nd digit is 2 the number of ways of selecting the other digits is 24
Arrangement, Number of ways
1, 2, 3, 4, 5, 6, 24
1, 4, 2, 18
1, 4, 5, 2, 12
1, 4, 5, 6, 2, 6
4, 1, 2, 18
4, 1, 5, 2, 12
4, 1, 5, 6, 6
4, 5, 1, 2, 12
4, 5, 1, 4, 2 6
4, 6, 5, 6
Total = 24 + 18 + 12 + 6 + 18 + 12 + 6 + 12 + 6 + 6 = 120 ways
The correct option is A. 120
2. The dimensions of the original rectangle = L by W
The dimensions of the lager rectangle = 1.5·L by 2·W
1.5·L × 2·W = 30
Given that L > W
∴ L×W = 30/(1.5 × 2) = 30/3 = 10
The possible integers that have a product of 10 are;
1 × 10 and 5 × 2
Therefore, since L > W, The dimensions of the larger rectangle are either 15 by 2 or 7.5 by 4
Which gives the perimeters as 2*(15 + 2) = 34 or 2*(7.5 + 4) = 23
Therefore, the largest possible rectangle is 34
The correct option is B. 34.