A) 28 | B) 14 |

C) 21 | D) 7 |

Explanation:

Let x, y, z be the number of balls received by the three persons, then

x + y + z =21

u + 5 + v + 5 + w + 5 = 21

u + v + w = 6

Total number of solutions =

A) 28450 | B) 26340 |

C) 32640 | D) 36450 |

Explanation:

We know that zero can't be in hundreds place. But let's assume that our number could start with zero.

The formula to find sum of all numbers in a permutation is

111 x no of ways numbers can be formed for a number at given position x sum of all given digits

No of 1 s depends on number of digits

So,the answer us

111 x 20 x (0+1+2+3+4+5) = 33300

We got 20 as follows. If we have 0 in units place we can form a number in 4*5 ways. This is for all numbers. So we have substituted 20 in formula.

Now, this is not the final answer because we have included 0 in hundreds place. so we have to remove the sum of all numbers that starts with 0.

This is nothing but the sum of all 2 digits numbers formed by 1 2 3 4 5. Because 0 at first place makes it a 2 digit number.

So the sum for this is 11 x 4 x (1+2+3+4+5).

=660

Hope u understood why we use 4. Each number can be formed in 4x1 ways

So, the final answer is 33300-660 = 32640

A) 28 | B) 56 |

C) 44 | D) 36 |

Explanation:

Given there are 9 flavours of ice creams.

Each child takes the combination of two flavours and no two children will have the same combination

This can be done by 9C2 ways i.e children.

Number of children = 9C2 = 9 x 8 / 2 = 36.

A) 360 | B) 420 |

C) 576 | D) 220 |

Explanation:

No. of letters in the word = 6

No. of 'E' repeated = 2

Total No. of arrangement = 6!/2! = 360

A) 26 | B) 54 |

C) 52 | D) 28 |

Explanation:

Number of mens = 8

Number of womens = 5

Different ways could couples be picked = 6c1 x 9c1 = 9 x 6 = 54 ways.

A) 521 | B) 720 |

C) 420 | D) 225 |

Explanation:

Let last digit is 2

when second last digit is 4 remaining 4 digits can be filled in 120 ways, similarly second last digit is 6 remained 4 digits can be filled in 120 ways.

so for last digit = 2, total numbers=240

Similarly for 4 and 6

When last digit = 4, total no. of ways =240

and last digit = 6, total no. of ways =240

so total of 720 even numbers are possible.