Question: In how many different ways can the letters of the word 'EXTENT' be arranged?
Options:
(A) 250
(B) 180
(C) 300
(D) 310
(E) 360
Ans: (B)
CoT: Number of ways = 6!/2!2! = 6X5X4X3X2X1/2X1X2X1 = 180
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Question: 10 people meet and shake hands. The maximum number of handshakes possible if there is to be no "cycle" of handshakes is (A cycle of handshakes is a sequence of k people a1, a2, , ak (k > 2) such that the pairs {a1, a2}, {a2, a3}, , {ak-1, ak}, {ak, a1} shake hands).
Options:
(A) 7
(B) 6
(C) 9
(D) 8
(E) 10
Ans: (C)
CoT: The question is not written in proper manner but we can work in 3 methods
1) If these are random handshakes, then total methods = 10*9/2*1 = 45
2) If these are cyclic handshakes, then total methods = 10
3) If these persons are not cyclic but they are arranged in a straight bench, then number of methods = 9
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Question: How many numbers can be made with digits 0, 7, 8 which are greater than 0 and less than a million?
Options:
(A) 496
(B) 486
(C) 1084
(D) 728
(E) 628
Ans: (D)
CoT: The number of single digit numbers = 2
The number of 2 digit numbers = 2 3 = 6
The number of 3 digit numbers = 2 3 3 = 18
The number of 4 digit numbers = 2 3 3 3 = 54
The number of 5 digit numbers = 2 3 3 3 3 = 162
The number of 6 digit numbers = 2 3 3 3 3 3 = 486
Therefore, the total numbers = 728
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