CUET PG 2025 — Mathematics PYQ

Step 1: Selecting Consonants

We need to select 3 consonants out of 5. Using the combination formula:

$C(5,3)=\frac{5!}{3!(5-3)!}=\frac{5!}{3!2!}$

Calculating the factorials:

$C(5,3)=\frac{5\times 4\times 3\times 2\times 1}{(3\times 2\times 1)\times (2\times 1)}=\frac{5\times 4}{2\times 1}=\frac{20}{2}=10$

There are 10 ways to choose the 3 consonants.

Step 2: Selecting Vowels

Next, we need to select 3 vowels out of the 4 available.

$C(4,3)=\frac{4!}{3!(4-3)!}=\frac{4!}{3!1!}$

Calculating the factorials:

$C(4,3)=\frac{4\times 3\times 2\times 1}{(3\times 2\times 1)\times 1}=\frac{4}{1}=4$

There are 4 ways to choose the 3 vowels.

Step 3: Total Number of Combinations

To find the total number of ways to select the group of letters (3 consonants and 3 vowels), we multiply the results from Step 1 and Step 2, according to the multiplication principle of counting.

Total number of ways = (Number of ways to choose consonants) × (Number of ways to choose vowels)

Total Ways = $C(5,3)\times C(4,3)=10\times 4=40$