Quantitative - Permutations and Combinations

Quantitative - Permutations and Combinations
Question:-
Option (A)
648
Option (B)
504
Option (C)
576
Option (D)
672
Correct Option:
A
Question Solution:
For the first digit you have 9 options (from 1 to 9 without 0), for the second number you have 9 options as well (0 to 9 minus the first digit that was already used) and for the third digit you have 8 options left.
So the number of possibilities is 9 x 9 x 8 = 648
Question:-
Option (A)
21
Option (B)
170
Option (C)
340
Option (D)
357
Correct Option:
B
Question Solution:
We have 20 vertices linking to 17 others each: that is 17*20=340. We divide that by 2 since every diagonal connects two vertices. 340/2=170. The vertex that does not connect to any diagonal is just not counted.
Question:-
Option (A)
1875
Option (B)
2000
Option (C)
2375
Option (D)
3875
Correct Option:
C
Question Solution:
Not considering the fact that 4 cannot appear more than once, we have a total of 4*5*5*5*5=2500. Now we deduct the possibilities where 4 does appear more than once (in this case it can appear only twice on the two leftmost even digits). In order to do so, we put 4 in the first and second leftmost digits. The rest of the digits are odd: 5*5*5=125. 2500-125=2375
Question:-
Option (A)
23
Option (B)
46
Option (C)
57
Option (D)
66
Correct Option:
D
Question Solution:
The worst case would be to take out 21 white balls, 22 green and 22 blue balls and still not having 23 of the same color. Take one more ball out and you get 23 of either the green or the blue balls. Notice that you cannot get 23 white balls since there are only 21, however, you must consider them since they might be taken out also.
The total is: 21+22+22+1= 66
Question:-
Option (A)
168
Option (B)
16
Option (C)
80
Option (D)
48
Correct Option:
C
Question Solution:
You must multiply your options to every item. (2 shelves) x (4 beds) x (3 closets + 7 chairs) = 80 possibilities
Question:-
Option (A)
246
Option (B)
248
Option (C)
492
Option (D)
15128
Correct Option:
C
Question Solution:
The phone company already created 122*122 area codes, now it can create 124*124.
1242-1222=(124+122)(124-122) = 246*2 = 492 additional codes

There are other ways to solve this question. However this way is usually the fastest.