1. ## challenge problems

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

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

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

In how many ways can 5 letters be posted in 3 post boxes, if any number of letters can be posted in all of the
three post boxes?

A. 5 C 3

B. 5 P 3

C. 53

D. 35

E. 25

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

There are 6 boxes numbered 1, 2 ...6. Each box is to be filled up either with a red or a green ball in such a way
that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The
total number of ways in which this can be done is
A. 5
B. 21
C. 33
D. 60
E. 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

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

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!

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!  Reply With Quote

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

Explanation: If we take all vowel as a single letter then BCS(AAU) total 4 letter can be arranged in 4! way.

Now three vowel can be arranged in 3!/2! ways. ( As in three vowel there is 2 'A' for this it is divided by 2!)
So total way is 4!*3!/2!  Reply With Quote

3. 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

There are four letter in math and we can rearrange this four letter in 4! ways.
And constant remain in order word is 4C
1 (math,amth, mtah and mtha) =4
So probability is 4/4
!=4/(4*3*2*1)=1/6  Reply With Quote

4. 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  Reply With Quote

5. 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!  Reply With Quote

6. There are 6 boxes numbered 1, 2 ...6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is
A. 5
B. 21
C. 33
D. 60
E. 6  Reply With Quote

7. 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

9. Is answer B 29 or 29????  Reply With Quote

8. Originally Posted by Md. Minuddin Q. In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear

together?

A.6!/2!

C.4!/2!

D.4!*3!/2!

B. 3!*3!
E.3!*3!/2!

understood the 4!*3! i.e. 3! is for vowels and 4! is for all letters. y is it divided by 2!.  Reply With Quote

9. Originally Posted by Md. Minuddin 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

Total arrangement=4!
With consonant in the same order=4

So probability is 4!/4

plz explain. i thought the answer is 1/24.  Reply With Quote

10. 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!

OA-A=7. not sure why  Reply With Quote