1How many arrangements can be made of the letters of the word “ASSASSINATION”? In how many of them are the vowels always together?

A$\dfrac{{13!}}{{{{\left( {4!} \right)}^2}}},\;\dfrac{{8! \times 6!}}{{{{\left( {4!} \right)}^2}}}$

B$\dfrac{{13!}}{{6! \times 7!}},\;\dfrac{{8! \times 6!}}{{{{\left( {4!} \right)}^2}}}$

C$\dfrac{{13!}}{{6! \times 7!}},\;\dfrac{{8! \times 6!}}{{6! \times 7!}}$

D$\dfrac{{13!}}{{{{\left( {4!} \right)}^2}}},\;\dfrac{{8! \times 6!}}{{6! \times 7!}}$

Show Answer

2In how many ways can the letters of the word ARRANGE be arranged so that two R’s are never together

A900

B360

C120

D1260

Show Answer

3In how many ways can the letters of the word ARRANGE be arranged so that The Two A’s are together but not two R’s

A900

B360

C240

D1260

Show Answer

4In how many ways can the letters of the word ARRANGE be arranged so that neither Two A’s nor two R's are together

A900

B360

C120

D660

Show Answer

5Ten different alphabets are given. Words containing five alphabets are to be formed from them. Find the number of words which have exactly one alphabet repeats.

A${}^{10}{P_5}$

B${\rm{10}}^{\rm{5}} $

C${10^5}{ - ^{10}}{P_5}$

D$58060$

Show Answer

6How many 4 letter words may be formed by using the letters of the word 'ASSASSINATION'

A916

B917

C360

D480

Show Answer

7How many numbers greater than a million can be formed by using the digits 2, 3, 0, 3, 5, 2, 3 which will be divisible by 5?

A110

B420

C720

D490

Show Answer

8 What is the sum of all five digit numbers formed by 2, 3, 4, 5, 6 without repetition?

A$20 × 5! × 11111$

B$20 × 3! × 11111$

C$20 × 4! × 11111$

D$20 × 4! × 10000$

Show Answer

9 What is the sum of all five digit numbers formed by 2, 3, 4, 5, 6 with repetition?

A$20 × {3^5} × 11111$

B$20 × {4^4} × 11111$

C$20 × {4^5} × 11111$

D$20 × {5^5} × 11111$

Show Answer

10 Find the sum of all the five digit numbers formed by the digits 2, 4, 6, 8, 0 with out repetition.

A3199960

B4199960

C5199960

D6199960

Show Answer

A$\dfrac{{13!}}{{{{\left( {4!} \right)}^2}}},\;\dfrac{{8! \times 6!}}{{{{\left( {4!} \right)}^2}}}$

B$\dfrac{{13!}}{{6! \times 7!}},\;\dfrac{{8! \times 6!}}{{{{\left( {4!} \right)}^2}}}$

C$\dfrac{{13!}}{{6! \times 7!}},\;\dfrac{{8! \times 6!}}{{6! \times 7!}}$

D$\dfrac{{13!}}{{{{\left( {4!} \right)}^2}}},\;\dfrac{{8! \times 6!}}{{6! \times 7!}}$

2In how many ways can the letters of the word ARRANGE be arranged so that two R’s are never together

A900

B360

C120

D1260

3In how many ways can the letters of the word ARRANGE be arranged so that The Two A’s are together but not two R’s

A900

B360

C240

D1260

4In how many ways can the letters of the word ARRANGE be arranged so that neither Two A’s nor two R's are together

A900

B360

C120

D660

5Ten different alphabets are given. Words containing five alphabets are to be formed from them. Find the number of words which have exactly one alphabet repeats.

A${}^{10}{P_5}$

B${\rm{10}}^{\rm{5}} $

C${10^5}{ - ^{10}}{P_5}$

D$58060$

6How many 4 letter words may be formed by using the letters of the word 'ASSASSINATION'

A916

B917

C360

D480

7How many numbers greater than a million can be formed by using the digits 2, 3, 0, 3, 5, 2, 3 which will be divisible by 5?

A110

B420

C720

D490

8 What is the sum of all five digit numbers formed by 2, 3, 4, 5, 6 without repetition?

A$20 × 5! × 11111$

B$20 × 3! × 11111$

C$20 × 4! × 11111$

D$20 × 4! × 10000$

9 What is the sum of all five digit numbers formed by 2, 3, 4, 5, 6 with repetition?

A$20 × {3^5} × 11111$

B$20 × {4^4} × 11111$

C$20 × {4^5} × 11111$

D$20 × {5^5} × 11111$

10 Find the sum of all the five digit numbers formed by the digits 2, 4, 6, 8, 0 with out repetition.

A3199960

B4199960

C5199960

D6199960