Probability

Answer :

There will be 2 cases

Case 1: 2 red, 1 blue or green

Prob. = 6C3 / 12C3 = 2/22

Add the cases, required prob. = 9/22 + 2/22 = 11/22 = 1/2

Answer :

Multiples of 4 up to 120 = 250/4 = 62 Multiples of 7 up to 120 = 250/7 = 35 (take only whole number before the decimal part)

Multiple of 28 (4x7) up to 250 = 250/28 = 8

So total such numbers are = 62 + 35 - 8 = 89

So required probability = 89/250

Answer :

There are 3*4 = 12 face cards in 52 cards So required probability = ¹²C₃ / ⁵²C₃ = 11/1105

Answer :

Total words that can be formed is 5! = 120 Now vowels together:

Take: S, P, T and AE

So their arrangement is 4! * 2! = 48

So required probability = 48/120 = 2/5

Answer :

Two cases:

Case 1: 0 at last place So 4 choices for 1st digit, 3 for 2nd, 2 for 3rd and 1 for 4th.

So numbers = 4*3*2*1 = 24

Case 2: 6 at last place

For 5-digit number 0 cannot be placed at

1st place or cannot be 1st digit

So 3 choices (1, 3, 5) for 1st digit, 3 for

2nd, 2 for 3rd and 1 for 4th.

So numbers = 3*3*2*1= 18

So total choices = 24+18 = 42 Number total 5-digit numbers that can be formed from 0, 1, 3, 5, and 6

0 not allowed at 1st place,

so 4 choices for 1st place, 4 for 2nd, 3 for 3rd, 2 for 4th and 1 for 5th.

Sp total = 4*4*3*2*1 = 96

So required probability = 42/96 = 7/16