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In the phrase "Military Institute of Science & Technology":
Number of words = 5 (Military, Institute, of, Science, Technology; treating '&' as a conjunction/symbol, or 6 if '&' is counted as a word).

If we count 5 words:
Total mass of graphite (pure carbon, C) required = $5 \times 5\text{ g} = 25\text{ g}$
Molar mass of carbon, $M = 12\text{ g/mol}$
Number of moles of carbon, $n = \frac{25}{12} = 2.0833\text{ mol}$

Number of carbon atoms = $n \times N_A = 2.0833 \times 6.022 \times 10^{23} \approx 1.255 \times 10^{24}\text{ atoms}$

(Alternatively, if '&' is counted as a separate word, total words = 6:
Total mass = $6 \times 5\text{ g} = 30\text{ g}$
Number of carbon atoms = $\frac{30}{12} \times 6.022 \times 10^{23} = 1.506 \times 10^{24}\text{ atoms}$).