Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4) = ( * )
= 210.
Number of groups, each having 3 consonants and 2 vowels = 210.
Each group contains 5 letters.
Number of ways of arranging 5 letters among themselves = 5! = 120
Required number of ways = (210 x 120) = 25200.
The smallest number in the series is 1000, a 4-digit number.
The largest number in the series is 4000, the only 4-digit number to start with 4.
The left most digit (thousands place) of each of the 4 digit numbers other than 4000 can take one of the 3 values 1 or 2 or 3.
The next 3 digits (hundreds, tens and units place) can take any of the 5 values 0 or 1 or 2 or 3 or 4.
Hence, there are 3 x 5 x 5 x 5 or 375 numbers from 1000 to 3999.
Including 4000, there will be 376 such numbers.
When at least 2 women are included.
The committee may consist of 3 women, 2 men : It can be done in ways
or, 4 women, 1 man : It can be done in ways
or, 2 women, 3 men : It can be done in ways.
Total number of ways of forming the committees
=
= 6 x 20 + 4 x 15 + 1x 6
= 120 + 60 + 6 =186
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