Quiz-1

Explanation:

A team of 6 members has to be selected from the 10 players. This can be done in 10C6 or 210 ways.
Now, the captain can be selected from these 6 players in 6 ways.
Therefore, total ways the selection can be made is 210*6 = 1260.

Explanation:

The word 'DETAIL' has 6 letters which has 3 vowels (EAI) and 3 consonants(DTL)
The 3 vowels(EAI) must occupy only the odd positions. Let's mark the positions as (1) (2) (3) (4) (5) (6). Now, the 3 vowels should only occupy the 3 positions marked as (1),(3) and (5) in any order.
Hence, number of ways to arrange these vowels
= 3P3
= 3!=3×2×1=6
Now we have 3 consonants(DTL) which can be arranged in the remaining 3 positions in any order. Hence, number of ways to arrange these consonants
= 3P3
=3!=3×2×1=6
Total number of ways
= number of ways to arrange the vowels × number of ways to arrange the consonants
=6×6=36

Explanation:

No. of Digits = 4 All are distinct; They can be arranged in 4! = 24 ways
Each of the digits 3, 4, 5 and 6 occur at unit place = 3! Ways = 6 ways.
Thus there will be 6 numbers ending with 3, 4, 5 and 6 each. So the sum of the digits at unit's place = 6(3 + 4 + 5 + 6) =108
The sum of numbers = 108 × 103 + 108 × 102 + 108 × 101 + 108 × 100 = 119988

Explanation:
The number of ways to select two men and three women = 5C2 * 6C3
= (5 *4 )/(2 * 1) * (6 * 5 * 4)/(3 * 2)
= 200

Explanation:

When 4 dice are rolled simultaneously, there will be a total of 64 = 1296 outcomes.
The number of outcomes in which none of the 4 dice show 3 will be 54 = 625 outcomes.
Therefore, the number of outcomes in which at least one die will show 3 = 1296 – 625 = 671

Explanation:

The number of ways of
Selecting A = 4+1 = 5
Selecting B = 2+1 = 3
Selecting C = 3+1 = 4
Selecting D = 1+1 = 2
Selecting E = 1+1 = 2
Selecting F = 1+1 = 2
Hence, total ways of selecting = 5 x 3 x 4 x 8 - 1 = 480 - 1 = 479

Explanation:

We are to choose 11 players including 1 wicket keeper and 4 bowlers or, 1 wicket keeper and 5 bowlers.
Number of ways of selecting 1 wicket keeper, 4 bowlers and 6 other players in 2C1*5C4*9C6 = 840
Number of ways of selecting 1 wicket keeper, 5 bowlers and 5 other players in 2C1*5C5*9C5 =252
Total number of ways of selecting the team = 840 + 252 = 1092

Explanation:

When 4 dice are rolled simultaneously, there are 64 = 1296 outcomes. The converse of what is asked in the question is that none of the dice show '6'. That is all four dice show any of the other 5 numbers. That is possible in 54 = 625 outcomes. Therefore, in 1296 - 625 = 671 outcomes at least one of the dice will show 6.

Explanation:

The word 'LOGARITHMS' has 10 different letters.
Hence, the number of 3-letter words(with or without meaning) formed by using these letters
= 10P3
= 10×9×8 = 720

Explanation:

Let n be the number of teams.
nC2 = 21
(n(n-1)/2) = 21
n(n-1) = 42
n = 7