Permutation And Combination Ques 7
Question-
Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?
(1) 24400
(2) 21300
(3) 210
(4) 25200
(5) None of these
(IBPS RRBs Officer CWE (Prelim Exam) 16.09.2017)
Show Answer
Correct Answer: (4)
Solution: (4)
Number of selections $=$ Selection of 3 consonants out of $7 \times$ selection of 2 vowels out of 4
= $7_{C_{3}} \times 4_{C_{2}}$
$=\frac{7 \times 6 \times 5}{1 \times 2 \times 3} \times \frac{4 \times 3}{1 \times 2}$ $=35 \times 6=210$
Now, 5 letters of each group can be arranged in 5 ! ways.
$\therefore$ Required answer $=210 \times 5$ ! $=210 \times 5 \times 4 \times 3 \times 2 \times 1$ $=25200$
BETA
