QB_PH_GA_017: Quantitative Aptitude

How many distinct 4-letter words (meaningful or non-meaningful) can be formed using the letters of the word 'VECTOR' without repetition of any letter?

Correct Answer

### Step-by-Step Derivation & Verification: 1. **Letter Inventory**: The word **VECTOR** consists of $n = 6$ letters: $\{V, E, C, T, O, R\}$, all of which are distinct. 2. **Arrangement Size**: Selecting and arranging $r = 4$ letters without repetition: $^n P_r = \frac{n!}{(n - r)!} = \frac{6!}{(6 - 4)!} = \frac{6!}{2!}$ 3. **Computation**: $^6 P_4 = 6 \times 5 \times 4 \times 3 = 360$ 4. **Official Integer Answer**: 360.