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Q:

# From a deck of 52 cards, a 7 card hand is dealt.How many distinct hands are there if the hand must contain 2 spades and 3 diamonds ?

 A) 7250100 B) 7690030 C) 7250000 D) 3454290

Explanation:

There are 13 spades,we must include 2: 13$C2$

There are 13 diamonds,we must include 3: $13C3$

Since we can't have more than 2 spades and 3 diamonds,the remaining 2 cards must be pulled out from the 26 remaining clubs and hearts : $26C2$

Therefore,$13C2*13C3*26C2$ = 7250100

Q:

In how many different ways can the letters of the word 'RITUAL' be arranged?

 A) 720 B) 5040 C) 360 D) 180

Explanation:

The number of letters in the given word RITUAL = 6

Then,

Required number of different ways can the letters of the word 'RITUAL' be arranged = 6!

=> 6 x 5 x 4 x 3 x 2 x 1 = 720

2 142
Q:

How many four digits numbers greater than 6000 can be made using the digits 0, 4, 2, 6 together with repetition.

 A) 64 B) 63 C) 62 D) 60

Explanation:

Given digits are 0, 4, 2, 6

Required 4 digit number should be greater than 6000.

So, first digit must be 6 only and the remaining three places can be filled by one of all the four digits.

This can be done by

1x4x4x4 = 64

Greater than 6000 means 6000 should not be there.

Hence, 64 - 1 = 63.

4 233
Q:

A card is drawn from a pack of 52 cards. What is the probability that either card is black or a king?

 A) 15/52 B) 17/26 C) 13/17 D) 15/26

Explanation:

Number of cards in a pack of cards = 52

Number of black cards = 26

Number of king cards = 4 (2 Red, 2 Black)

Required, the probability that if a card is drawn either card is black or a king =

4 335
Q:

A box contains 2 blue balls, 3 green balls and 4 yellow balls. In how many ways can 3 balls be drawn from the box, if at least one green ball is to be included in the draw?

 A) 48 B) 24 C) 64 D) 32

Explanation:

Total number of balls = 2 + 3 + 4 = 9

Total number of ways 3 balls can be drawn from 9 = 9C3

No green ball is drawn = 9 - 3 = 6 = 6C3

Required number of ways if atleast one green ball is to be included = Total number of ways - No green ball is drawn

= 9C3 - 6C3

= 9x8x7/3x2  -  6x5x4/3x2

= 84 - 20

= 64 ways.

4 443
Q:

How many 4-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?

 A) 60 B) 48 C) 36 D) 20

Explanation:

Here given the required digit number is 4 digit.

It must be divisible by 5. Hence, the unit's digit in the required 4 digit number must be 0 or 5. But here only 5 is available.

x x x 5

The remaining places can be filled by remaining digits as 5 x 4 x 3 ways.

Hence, number 4-digit numbers can be formed are 5 x 4 x 3 = 20 x 3 = 60.

1 439
Q:

In how many ways the word 'SCOOTY' can be arranged such that 'S' and 'Y' are always at two ends?

 A) 720 B) 360 C) 120 D) 24

Explanation:

Given word is SCOOTY

ATQ,

Except S & Y number of letters are 4(C 2O's T)

Hence, required number of arrangements = 4!/2! x 2! = 4!

= 4 x 3 x 2

= 24 ways.

3 714
Q:

In how many ways word of 'GLACIOUS' can be arranged such that 'C' always comes at end?

 A) 3360 B) 5040 C) 720 D) 1080

Explanation:

Given word is GLACIOUS has 8 letters.

=> C is fixed in one of the 8 places

Then, the remaining 7 letters can be arranged in 7! ways = 5040.

2 872
Q:

From a group of 7 boys and 6 girls, five persons are to be selected to form a team, so that at least 3 girls are there in the team. In how many ways can it be done?

 A) 427 B) 531 C) 651 D) 714

Explanation:

Given in the question that, there are 7 boys and 6 girls.

Team members = 5

Now, required number of ways in which a team of 5 having atleast 3 girls in the team =