Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?Question 18Answera.25200b.22500c.Noned.22220
Question
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
Question 18
Answer
- a. 25200
- b. 22500
- c. None
- d. 22220
Solution
To solve this problem, we need to use the concept of combinations in probability.
Step 1: Select 3 consonants out of 7 This can be done in 7C3 ways. The formula for combinations is nCr = n! / r!(n-r)!. Here, n is the total number of items, and r is the number of items to choose. So, 7C3 = 7! / 3!(7-3)! = 35 ways.
Step 2: Select 2 vowels out of 4 This can be done in 4C2 ways. So, 4C2 = 4! / 2!(4-2)! = 6 ways.
Step 3: Arrange the selected consonants and vowels We have 5 letters (3 consonants and 2 vowels), which can be arranged in 5! = 120 ways.
Step 4: Multiply the results of steps 1, 2, and 3 The total number of words is 35 (from step 1) * 6 (from step 2) * 120 (from step 3) = 25200.
So, the answer is a. 25200.
Similar Questions
Q 4 N S E # K 7 Y $ C 8 3 P I T 6 % 9 H U 2 R J * V 5 W A 1 B D G How many such vowels are there each of which are immediately followed by a symbol?
How many different words can be formed using the letters of the word “EDUCATION‘ such that , the word always ends with a vowel?
In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?A360B480C720D5040ENone of these
If two letters are taken at random from the word HOME, what is theProbability that none of the letters would be vowels?(a) 1/6(b) 1/2(c) 1/3(d) ¼
n how many different ways may the seven letters in the word KARACHI be arranged, if all of the letters are used each time?A.2500B.2520C.2420D.2400
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.