 Originally Posted by Md. Minuddin In how many ways can the letters of the word “PROBLEM” be rearranged to make 7 letter words such that
none of the letters repeat?

A. 7

B. 7C7
C. 77
D. 49
E. None of these

Answer should be E. Because the actual result should 7!

The question says - 'none of the letters repeat'...this shuld be reg the positions(atleast from OG perspective).
so, according to OG it is 7 instead of 7!

1 -- PROBLEM
2 -- ROBLEM P
3 -- 0BLEM PR
and so on.... which will stop after 7th combination.

Not sure how excatly do we need to interpret this question...!!! Any inputs...?

thank you.  Reply With Quote

2. Originally Posted by givinggmat The question says - 'none of the letters repeat'...this shuld be reg the positions(atleast from OG perspective).
so, according to OG it is 7 instead of 7!

1 -- PROBLEM
2 -- ROBLEM P
3 -- 0BLEM PR
and so on.... which will stop after 7th combination.

Not sure how excatly do we need to interpret this question...!!! Any inputs...?

thank you.
PROBLEM has 7 letter which is different from each other

1----2---3----4---5----6---7

Actually I think repeat means using same letter more then once. If so then for first position we have 7 choice. As we can't repeat same letter so now from the rest 6 letter we can choice second position in 6 way
And so on,
So total way 7*6*5*4*3*2*1=7!  Reply With Quote

3. How many different positive integers exist between 10^6and 10^7, the sum of whose digits is equal to 2?
A. 6
B. 7
C. 5
D. 8
E. 18

110000
101000
100100
100010
100001
200000  Reply With Quote

4. Ten coins are tossed simultaneously. In how many of the outcomes will the third coin turn up a head?
A. 210
B. 29
C. 3*28
D. 3*29
E. None of these  Reply With Quote

5. A man can hit a target once in 4 shots. If he fires 4 shots in succession, what is the probability that he will hit
his target?
A. 1
B.1/256
C.81/256
D.175/256
E.108/256

1/4 * 1/4 * 1/4 * 1/4 = 1/256  Reply With Quote

6. What is the probability that the position in which the consonants appear remain unchanged when the letters of
the word Math are re-arranged?
A. 1/4
B. 1/6
C. 1/3
D. 1/24
E. 1/12

E. 1/12  Reply With Quote

7. In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear
together?
A.6!/2!
B. 3!*3!
C.4!/2!
D.4!*3!/2!
E.3!*3!/2!

(AAu)BCS => can be arranged in 4! ways..
then AAU can be arranged in 3!/2! ways
total 4!*3!/2!  Reply With Quote

8. How many different four letter words can be formed (the words need not be meaningful) using the letters of the word MEDITERRANEAN such that the first letter is E and the last letter is R?
A. 59
B.11!/3!*2!*2!*2!
C. 56
D. 23
E.11!/2!*2!*2!
before using, the number of times alphabet appear is
m=1; e=3; r=2; a=2; n=2; d=1; i=1; t=1

We make the word E _ _ R so number of times E and R is reduced by 1
so m=1; e=2; r=1; a=2; n=2; d=1; i=1; t=1

total combinations = 11!/2!*2!*2!  Reply With Quote

9. Originally Posted by abhishek_mumbai How many different positive integers exist between 10^6and 10^7, the sum of whose digits is equal to 2?
A. 6
B. 7
C. 5
D. 8
E. 18

110000
101000
100100
100010
100001
200000
106= 1000000
107= 10000000

There is
1000001
1000010
1000100
1001000
1010000
1100000
2000000  Reply With Quote

10. How many different positive integers exist between 10^6and 10^7, the sum of whose digits is equal to 2?
A. 6
B. 7
C. 5
D. 8
E. 18

10^6=1000000 , 10^7= 10000000
any integer between these two values will have 7 digits
for a 7 digit number to have 2 as sum of its digits, there are only two possibilities :
1) one of the digits has to be 2 and the rest 0...for the number to remain a 7 digits number, that one digit has to be the left most one..hence it should be 2000000
2)two of the digits have to be 1 and the rest 0..for the number to remain a 7 digit number, the leftmost digit has to be 1..and of the other six positions, 1 of them have to be 1 and the rest 0..there are 6 such possibilities (6C1)  Reply With Quote